# Non-zero Temperature and Density

Continuum EoS for QCD with $$N_f=2+1$$ flavors
Stefan Krieg
Mon, 14:00, Seminar Room A -- Parallels 1A (Slides)

We present and discuss continuum extrapolated results for the $$N_f=2+1$$ equation of state. We compare our findings with our previously published results as well as other results in the literature.

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Freeze-out parameters from continuum extrapolation
Szabolcs Borsanyi, Zoltan Fodor, Sandor Katz, Prof Claudia Ratti
Mon, 14:20, Seminar Room A -- Parallels 1A (Slides)

Based on lattice simulations with stout staggered fermions we calculate the continuum limit for various second and higher order fluctuations of conserved charges, like electric charge, baryon number and strangeness. These can be related to direct experimental observables that have been measured by RHIC experiments. We give a numerical estimate for the freeze-out parameters as a function of beam energy and discuss the flavor specific nature of the calculated fluctuations.

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Chiral phase transition of $$N_f=2+1$$ QCD with the HISQ action
Heng-Tong Ding
Mon, 14:40, Seminar Room A -- Parallels 1A (Slides)

We will present studies of universal properties of the chiral phase transition in $$N_f=2+1$$ QCD based on the simulations using Highly Improved Staggered fermions on lattices with temporal extent $$N_t=6$$. We analyze the quark mass and volume dependence of the chiral condensates and chiral susceptibilities in QCD with two degenerate light quarks and a strange quark. The strange quark mass is chosen to be fixed to its physical value (ms) and five values of light quark masses (ml) that are varied in the interval $$1/20 \geq ml/ms \geq 1/80$$. Here various quark masses correspond to pseudo Goldstone pion masses ranging from about 160 MeV to about 80 MeV. The O(N) scaling of chiral observables and the influence of universal scaling on physical observables in the region of physical quark mass values are also discussed. *This work is based on the collaboration with A. Bazavov, Y. Maezawa, S. Mukherjee, F. Karsch and P. Petreczky.

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Quark number susceptibilities at high temperatures
Peter Petreczky
Mon, 15:00, Seminar Room A -- Parallels 1A (Slides)

We present continuum extrapolated results of second order quark number susceptibilities from calculations using the HISQ action and of fourth order quark number susceptibilities from calculations using the p4 action in 2+1 flavor QCD in the high temperature region of 200 MeV $$< T <$$ 1 GeV. Simulations has been performed at nearly physical quark mass having $$m_\pi L >3$$ with temporal extent $$N_t=6,8,10,12$$ and $$16$$ using the HISQ action and with temporal extent $$N_t=6,8$$ and $$12$$ using the p4 action. We compare the continuum extrapolated results with resummed perturbative calculations. Implications of our findings on the range of validity of high temperature perturbation theory will be discussed.

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Charge Fluctuations as Thermometer for Heavy-Ion Collisions
Mathias Wagner
Mon, 15:20, Seminar Room A -- Parallels 1A (Slides)

We present a determination of freeze-out conditions in heavy-ion collisions based on ratios of cumulants of net electric charge fluctuations obtained from lattice QCD. These ratios can reliably be calculated for a wide range of chemical potential values by using a next-to-leading order Taylor series expansion around the limit of vanishing baryon, electric charge and strangeness chemical potentials. We first determine the strangeness and electric charge chemical potentials that characterize the conditions in heavy ion collisions at RHIC and LHC. We then show that a comparison of lattice QCD results for ratios of up to third order cumulants of electric charge fluctuations with experimental results allows us to extract the freeze-out baryon chemical potential and the freeze-out temperature. We apply our method [1] to preliminary data of the STAR and PHENIX collaborations. [1] A.Bazavov et al., Phys.Rev.Lett.109, 192302 (2012).

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The QCD Phase Transition with Domain Wall Fermions and Physical Pion Masses
Chris Schroeder
Mon, 15:40, Seminar Room A -- Parallels 1A (Slides)

The HotQCD collaboration has extended its study of the finite temperature transition in 2+1 flavor QCD using domain wall fermions (DWF) to the physical point. With chiral fermions and three degenerate, physical-mass pions, these calculations are arguably the most realistic of their kind to date - enabled by the LLNL/IBM 20 Petaflops Sequoia Blue Gene/Q, highly optimized BAGEL/CPS software, and algorithmic advances, in particular, the dislocation suppressing determinant ratio (DSDR). All results are for a fixed temporal lattice size, $$N_\tau=8$$, yet discretization effects, at least for the spectrum at zero temperature, are expected to be at the 5% level. I will present near-final results for the disconnected light-quark chiral susceptibility for spatial extent $$L \approx 4/m_\pi$$ and preliminary results for $$L \approx 8/m_\pi$$. I will also describe recent developments pertaining to ongoing work using 200 MeV pions as well as a nascent investigation into the possibility of a first-order phase transition at lower pion masses.

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Momentum broadening of partons on the light cone from the lattice
Marco Panero, Kari Rummukainen, Andreas Schäfer
Mon, 16:30, Seminar Room A -- Parallels 2A (Slides)

The jet-quenching parameter describes the momentum broadening of a high-energy parton moving through the quark-gluon plasma. Following an approach originally proposed by Caron-Huot, we discuss how one can extract information on the collision kernel associated with the parton momentum broadening, from the analysis of certain gauge-invariant operators in dimensionally reduced effective theories, and present numerical results from a lattice study.

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The sign problem and Abelian lattice duality
Michael Ogilvie, Peter Meisinger
Mon, 16:30, Seminar Room B -- Parallels 2B (Slides)

For a large class of Abelian lattice models with sign problems, including the case of non-zero chemical potential, duality maps models with complex actions into dual models with real actions. For extended regions of parameter space, calculable for each model, duality resolves the sign problem for both analytic methods and computer simulations. Explicit duality relations are given for models for spin and gauge models based on Z(N) and U(1) symmetry groups. The dual forms are generalizations of the Z(N) chiral clock model and the lattice Frenkel-Kontorova model, respectively. From these equivalences, rich sets of spatially-modulated phases are found in the strong-coupling region of the original models.

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Towards understanding thermal jet quenching via lattice simulations
Alexander Rothkopf, Mikko Laine
Mon, 16:50, Seminar Room A -- Parallels 2A (Slides)

Motivated by its connection to the collisional broadening of jets in heavy ion collisions, we study the real-time evolution of a light-cone Wilson loop in classical lattice gauge theory. The associated transport coefficient, traditionally denoted by $$\hat{q}$$, is related to a collision kernel $$C({\bf x}_\perp)$$ which in real time can be extracted from the damping rate of the light-cone Wilson loop. Numerical results for $$C({\bf x}_\perp)$$ are contrasted with perturbative estimates. We also observe that tilting the Wilson loop beyond the light cone does not change its qualitative behaviour, which strengthens arguments in the literature on the applicability of dimensional reduction for a refined determination of $$C({\bf x}_\perp)$$.

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Dual Methods for Lattice Field Theories at Finite Density
Thomas Kloiber, Christof Gattringer
Mon, 16:50, Seminar Room B -- Parallels 2B (Slides)

When studying (lattice) field theories at finite densities, the notorious complex action or sign problem arises, i.e., the action becomes complex for non-vanishing chemical potential. Therefore the Boltzmann factor also becomes complex, which spoils a probabilistic interpretation. To get rid of complex contributions to the partition function we reformulate the theory in terms of new degrees of freedom -- so-called dual variables. In this representation the partition function consists of real, non-negative contributions only, such that a probabilistic interpretation is feasible. The fundamental degrees of freedom are then integer-valued and constrained. Here we treat a complex (charged) $$\phi^4$$ theory, i.e., the relativistic Bose gas. We show how the dual representation is derived and discuss its numerical simulation which generates only admissible configurations. This is achieved with a generalized version of the Prokof'ev-Svistunov worm algorithm. Physical phenomena like the Silver Blaze problem and Bose condensation can then be studied efficiently. In addition, we present a method to extract n-point functions from the dual ensemble. Results for the field correlators and finite chemical potential spectroscopy calculations are shown.

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Temperature dependence of electrical conductivity and dilepton rates from hot quenched lattice QCD
Olaf Kaczmarek
Mon, 17:10, Seminar Room A -- Parallels 2A (Slides)

We present new results on the continuum extrapolation of the vector current correlation function in the deconfined phase for three temperatures close to the critical temperature utilizing quenched clover improved Wilson fermions and light quark masses. A systematic analysis on multiple lattice spacing allows to perform the continuum limit of the correlation function and to extract spectral properties in the continuum limit. These results provide constrains for the electrical conductivity and the thermal dilepton rates in the quark gluon plasma for the given temperature range. In addition preliminary results on the continuum extrapolation at finite momenta related to thermal photon rates will be presented.

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A property of fermions at finite density by a reduction formula of fermion determinant
Keitaro Nagata, Shoji Hashimoto, Atsushi Nakamura
Mon, 17:10, Seminar Room B -- Parallels 2B (Slides)

A reduction formula of the fermion determinant, which is derived by calculating temporal part of the fermion determinant analytically, provides a reduced matrix which describes the propagation of quarks from initial to final time. We derive the Gauss's law for a free energy and eigenvalues of the reduction formula. This provides a correspondence between the reduction formula and two dimensional electrostatic problem. We discuss a property of fermions using this correspondence for finite density QCD.

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Transport Coefficients of the QGP
Alessandro Amato, Gert Aarts, Chris Allton, Pietro Giudice, Simon Hands, Jon-Ivar Skullerud
Mon, 17:30, Seminar Room A -- Parallels 2A (Slides)

A lattice calculation is presented for the electrical conductivity of the QCD plasma at finite temperature, using a tadpole improved clover action with 2+1 dynamical flavours and conserved currents. The behaviour of this transport coefficient is shown over a wide range of temperatures, across the deconfining transition. The spectral functions relevant for the analysis are extracted using the MEM algorithm, with a detailed investigation of its systematics.

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QCD at imaginary chemical potential with Wilson fermions
Andrei Alexandru, Anyi Li
Mon, 17:30, Seminar Room B -- Parallels 2B (Slides)

The phase diagram for QCD at non-zero baryon density is difficult to explore using lattice QCD techniques due to the sign problem. One possible avenue to constrain the features in this diagram is through simulations at imaginary chemical potential where numerical simulations are possible. Most numerical investigations in this region use staggered fermions, which are problematic for systems where the number of flavors is not a multiple of four. In this study, we use Wilson fermions to investigate the phase diagram for QCD with three degenerate flavors of quarks. We use a determinant compression method to perform a multi-histogram reweighting in both temperature and imaginary chemical potential, which allows us to smoothly map out this region. We identify the endpoint of the Roberge-Weise transition line and determine its relation to the pseudo-critical curve that intersects the zero-density line. We compare these results with results from another study at real chemical potential.

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Lattice computation of the transport coefficient kappa in pure Yang-Mills theory
Christian Schäfer, Owe Philipsen
Mon, 17:50, Seminar Room A -- Parallels 2A (Slides)

From heavy-ion collision experiments we know that the quark-gluon plasma behaves almost like an ideal fluid and can be described by hydrodynamics. The dynamic properties of the quark-gluon plasma are determined by transport coefficients. The second order transport coefficient kappa is related to a momentum expansion of the euclidean energy-momentum tensor correlator at vanishing Matsubara frequency. The computation of the Fourier-transformed correlator in lattice gauge theory allows the determination of kappa from first principles. We present the results obtained by pure Yang-Mills lattice simulations in comparison to a computation in quasi-free lattice perturbation theory as well as the temperature dependence of the transport coefficient kappa.

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The nature of the Roberge-Weiss transition in $$N_f=2$$ QCD with Wilson fermions
Christopher Pinke, Owe Philipsen
Mon, 17:50, Seminar Room B -- Parallels 2B (Slides)

QCD at imaginary chemical potential can be simulated without a sign problem and possesses a rich phase structure. In particular, the Roberge-Weiss transition between neighbouring $$Z(N_c)$$ sectors is connected to the analytic continuation of the chiral and deconfinement transitions at small and large quark masses, respectively, thus constraining the phase diagram at real chemical potential. We investigate the nature of this connection as a function of the quark mass using Wilson fermions and finite size scaling on $$N_t=4$$ lattices.

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Non-Equilibrium Fermion Production on the Lattice
Daniil Gelfand, Jürgen Berges, Florian Hebenstreit
Mon, 18:10, Seminar Room A -- Parallels 2A (Slides)

We present a modern approach to far from equilibrium fermion production using real-time simulations. This method is applied to study quark production from bosonic instabilities in QCD and effective models as well as pair production in abelian gauge theories. We discuss the role of quantum effects in presence of non-perturbatively high bosonic fluctuations and compare to approximative descriptions based on homogeneous background fields. Both strongly and weakly coupled scenarios are considered and the emergence of power-law and Fermi-Dirac distributions of quark occupation numbers is observed. The latter result is being used to define a non-equilibrium quasi-temperature for quarks. In 1+1 dimensional QED we are able to investigate the build-up of a linear rising potential between produced fermion bunches and the striking phenomenon of dynamical string breaking, which strongly resembles the corresponding effect in QCD.

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Singularities around the QCD critical point in the complex chemical potential plane
Hiroshi Yoneyama, Shinji Ejiri, Yasuhiko Shinno
Mon, 18:10, Seminar Room B -- Parallels 2B (Slides)

The thermodynamic singularities appearing in the complex chemical potential $$\mu$$ plane provide us with useful information on the phase structure and also control the validity of the simulation method in the lattice calculations. In order to investigate the phase structure in the vicinity of the critical end point (CEP) in finite density QCD, we resort to an effective theory based on a mean filed approach, and discuss what the singularities are like in the complex $$\mu$$ plane. By focusing on the real part of the free energy described by the complex order parameter in the complex $$\mu$$ plane, we explicitly investigate the structure of the singularities and of the Stokes lines associated them. This provides us with useful information concerning the distributions of the Lee-Yang zeros in finite volumes. The behavior of the chiral and quark number susceptibilities around the singular point is also discussed.

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Towards lattice studies of anomalous transport
Pavel Buividovich
Mon, 18:30, Seminar Room A -- Parallels 2A (Slides)

The methods of studying anomalous transport phenomena (such as the chiral magnetic or the chiral vortical effects) in lattice gauge theories are discussed. Since anomalous transport is a ground-state property, it is ideally suited for lattice studies in Euclidean space - e.g. there is no need to perform analytic continuation in order to find the corresponding spectral functions. I discuss definitions of anomalous transport coefficients based on static current-current correlators and on the current expectation values in the presence of external magnetic field and clarify their relation to axial anomaly. It is argued that transport coefficients obtained from simulations with constant background magnetic field are incompatible with those obtained from static current-current correlators.

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Lattice QCD at finite isospin chemical potential
Chiho Nonaka, Masaki Kondo
Mon, 18:30, Seminar Room B -- Parallels 2B (Slides)

Many attempts have been made to solve the sign problem at finite density lattice QCD. Some of them succeed in applying to high temperature and low density region of the QCD phase diagram and giving us insight of the QCD phase transition. However they can not be applied to the low temperature and high density region where theories with positive fermion determinants such as imaginary chemical potential, two-color QCD and isospin chemical potential are useful. Here we investigate detailed meson properties at finite isospin chemical potential. We include the source term which breaks the explicit isospin symmetry into the Wilson fermion to keep the positive fermion determinant and carry out the hybrid monte carlo simulation. In particular, we will discuss the possibility of pion condensation and rho meson condensation at finite isospin chemical potential.

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Continuity of the Deconfinement Transition in (Super) Yang Mills Theory
Thomas Schaefer
Mon, 18:50, Seminar Room B -- Parallels 2B (Slides)

We study the phase diagram of SU(2) Yang-Mills theory with one adjoint Weyl fermion on $$R^3\times S^1$$ as a function of the fermion mass m and the compactification scale beta. This theory reduces to thermal pure gauge theory as $$m\to\infty$$ and to circle-compactified (twisted) susy gluodynamics in the limit $$m\to 0$$. In the $$m-L$$ plane, there is a line of center symmetry changing phase transitions. In the limit $$m\to\infty$$, this transition takes place at $$\beta_c=1/T_c$$, where $$T_c$$ is the critical temperature of the deconfinement transition in pure Yang-Mills theory. We show that near $$m=0$$, the critical scale $$\beta_c$$ can be computed using semi-classical methods and that the transition is of second order. This suggests that the deconfining phase transition in pure Yang-Mills theory is continuously connected to a phase transition that can be studied in weak coupling. The center symmetry changing phase transition arises from the competition of perturbative effects, fractionally charged instantons, and instanton molecules. The calculation can be extended to higher rank gauge groups and non-zero theta angle. (This is work done in collaboration with M. Unsal and E. Poppitz).

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Meson screening masses at finite temperature with Highly Improved Staggered Quarks
Yu Maezawa
Tue, 14:00, Seminar Room A -- Parallels 3A (Slides)

We study meson screening masses at finite temperature in 2+1 flavor QCD using the Highly Improved Staggered Quarks (HISQ) action. The screening masses are obtained from spatial meson propagators and enable us to probe the sensitivity of hadronic correlation functions to the quark structure in thermal matter. We calculate the meson screening masses on lattices with aspect ratio $$N_s/N_t = 4$$ in a larger temperature interval of 140-250 MeV for $$N_t=12$$ and 250-740 MeV for $$N_t=4-10$$. We focus on the strange and charmed flavor sectors and find that significant modifications of thermal masses in the strange quark sector appear even below the critical temperature ($$T_c$$), whereas for charmonium states modifications become significant only for $$T > 1.2T_c$$. We also present several other properties of meson states at finite temperature, e.g. modifications of amplitudes and the onset of spin and parity degeneracy at high temperature.

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The thermodynamic and continuum limit of meson screening masses
Marcel Müller, Olaf Kaczmarek, Edwin Laermann
Tue, 14:20, Seminar Room A -- Parallels 3A (Slides)

We present results on the thermodynamic and continuum limit of meson screening masses in the deconfined phase, using standard staggered and non-perturbatively clover-improved Wilson fermions in the quenched approximation with light quark masses. For two temperatures, $$1.5 T_c$$ and $$3.0 T_c$$, it is found that on finite lattices screening masses differ between the actions. We study if both actions reproduce the same masses in the continuum by employing different methods of extrapolation to the thermodynamic and continuum limit.

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2+1 flavour thermal studies on an anisotropic lattice
Chris Allton, Gert Aarts, Alessandro Amato, Pietro Giudice, Simon Hands, Sinead Ryan, Jon-Ivar Skullerud
Tue, 14:40, Seminar Room A -- Parallels 3A (Slides)

The FASTSUM collaboration has initiated a detailed study of thermal QCD using 2+1 flavours of Wilson quarks on an anisotropic lattice. Spatial volumes of $$24^3$$ and $$32^3$$ are used at fixed cut-off with temperatures ranging from 120 to 360 MeV (corresponding to temporal lattice extents of 48 to 16 lattice units). Results of the chiral susceptibility, deconfinement temperature, and restoration of chiral symmetry will be presented.

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The strange degrees of freedom in QCD at high temperature
Christian Schmidt
Tue, 15:00, Seminar Room A -- Parallels 3A (Slides)

We use appropriate combinations of conserved charge fluctuations up to the fourth order to probe the strangeness carrying degrees of freedom in QCD at high temperature. In particular, we use diagonal fluctuations of net strangeness as well as their correlations with net baryon number and net electric charge, which we have obtained from lattice QCD calculations using 2+1 flavor of highly improved staggered quarks (HSIQ) on $$N_t=6$$ and $$8$$ lattices. We show that up to the chiral crossover temperature ($$T_c$$) strange mesons and baryons, can be well described by an uncorrelated gas of hadrons. On the other hand, the strangeness carrying degrees of freedom inside the quark gluon plasma can be described by a weakly interacting gas of quarks only for temperatures larger than $$2 T_c$$. In the intermediate temperature window these observables show considerably richer structures, indicative of the strongly interacting nature of the quark gluon plasma.

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Thermodynamics with $$N_f=2+1+1$$ twisted mass quarks
Florian Burger, Ernst-Michael Ilgenfritz, Maria Paola Lombardo, Michael Muller-Preussker
Tue, 15:20, Seminar Room A -- Parallels 3A (Slides)

We present first results of QCD thermodynamics with dynamical first and second quark family obtained within the fixed-scale approach. We are investigating several small lattice spacings in order to check for and quantify discretization effects.

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Update on the 2+1+1 flavor QCD equation of state with HISQ
Alexei Bazavov, Claude Bernard, Carleton DeTar, Justin Foley, Steven Gottlieb, Urs Heller, James Hetrick, Laiho Jack, Doctor Ludmila Levkova, James Osborn, Robert Sugar, Doug Toussaint, Ruth van de Water, Ran Zhou
Tue, 15:40, Seminar Room A -- Parallels 3A

We present recent results on the QCD equation of state with 2+1+1 flavors of highly improved staggered quarks (HISQ). We focus on three sets of ensembles with temporal extent $$N_t=6, 8$$ and $$10$$, that reach up to temperatures of 967, 725 and 580 MeV, respectively. The strange and charm quark masses are tuned to the physical values and the light quarks mass is set to one fifth of the strange. (This corresponds to the Goldstone pion of about 300 MeV.)

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Scale hierarchy in high-temperature QCD
Philippe de Forcrand, Oscar Akerlund
Tue, 16:20, Seminar Room A -- Parallels 4A (Slides)

Because of asymptotic freedom, QCD becomes weakly interacting at high temperature: this is the reason for the transition to a deconfined phase in Yang-Mills theory at temperature $$T_c$$. At high temperature $$T \gg T_c$$, the smallness of the coupling $$g$$ induces a hierachy betwen the "hard", "soft" and "ultrasoft" energy scales $$T$$, $$g T$$ and $$g^2 T$$. This hierarchy allows for a very successful effective treatment where the "hard" and the "soft" modes are successively integrated out. However, it is not clear how high a temperature is necessary to achieve such a scale hierarchy. By numerical simulations, we show that the required temperatures are extremely high. Thus, the quantitative success of the effective theory down to temperatures of a few $$T_c$$ appears surprising a posteriori.

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Many-flavor Schwinger model at finite chemical potential
Robert Lohmayer, Rajamani Narayanan
Tue, 16:40, Seminar Room A -- Parallels 4A (Slides)

We study thermodynamic properties of the massless Schwinger model on a torus at finite chemical potential. Generalizing the two-flavor case, we derive analytic expressions for an arbitrary number of fermion flavors and discuss physical results for three and four flavors in detail.

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Nature of finite temperature and density phase transitions in many-flavor QCD
Tue, 17:00, Seminar Room A -- Parallels 4A (Slides)

To discuss the feasibility of the electroweak baryogenesis in realistic technicolor scenario, we investigate the phase structure of $$(2+N_f)$$-flavor QCD, where two light flavors and $$N_f$$ massive flavors exist. Because an appearance of a first order phase transition at finite temperature is a necessary condition for the baryogenesis, it is important to study the nature of finite temperature phase transition. Applying the reweighting method, the probability distribution function of the plaquette is calculated in the many-flavor QCD. Through the shape of the distribution function, we determine the critical mass of heavy flavors terminating the first order region, and find it to become larger with $$N_f$$. We moreover study the critical line at finite density and the first order region is found to become wider as increasing the chemical potential. This may be a good test for the determination of boundary of the first order region in (2+1)-flavor QCD at finite density.

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Solving the sign problem of scalar, two-flavored electrodynamics for finite chemical potential and exploring its full phase-diagram.
Alexander Schmidt, Ydalia Delgado, Christof Gattringer
Tue, 17:20, Seminar Room A -- Parallels 4A (Slides)

On the lattice we explore two-flavored, scalar electrodynamics, which has a sign-problem for finite chemical potential. Rewriting the action in terms of dual variables we can solve this sign problem exactly. The dual variables are links and plaquettes, subject to non-trivial constraints, which have to be respected by the simulation-algorithm. We here use a local Monte-Carlo-algorithm to perform simulations in the dual representation and study the full phase-diagram of the model.

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Surface worm algorithm for Abelian Gauge-Higgs systems at finite density
Ydalia Delgado, Christof Gattringer, Alexander Schmidt
Tue, 17:40, Seminar Room A -- Parallels 4A (Slides)

We present the surface worm algorithm (SWA), which is a generalization of the Prokof'ev Svistunov worm algorithm concept to simulate abelian Gauge-Higgs models on a lattice which can be mapped to systems of surfaces and loops (dual representation). First we assess the performance of the SWA using a U(1) Gauge-Higgs model and compare it with a local update in the dual representation. Then we also perform simulations of scalar electrodynamics with two flavors at finite density, where the sign problem is overcome in the dual representation.

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Simulating full QCD at nonzero density using The Complex Langevin Equation
Denes Sexty
Wed, 08:30, Seminar Room A -- Parallels 5A (Slides)

We employ a new method, "gauge cooling", to stabilize complex Langevin simulations of QCD. First the heavy quark approximation is investigated, where results are checked against results obtained with reweigthing; then the method is extended to full QCD with light quarks. The method allows us to go to previously unaccessible high densities.

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Magnetic-field induced (inverse) catalysis for gluons through an improved interaction measure
Falk Bruckmann, Gunnar S. Bali, Gergely Endrodi, Schafer Andreas, Florian Gruber
Wed, 08:30, Seminar Room B -- Parallels 5B (Slides)

We analyze the influence of external magnetic fields on the gluonic action and the quark condensate at zero temperature -- catalysis -- and around the transition -- inverse catalysis -- from $$N_f=1+1+1$$ staggered quarks of physical masses. We also show how both quantities can be used to improve the scaling properties of the interaction measure (trace anomaly).

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Localised distributions in complex Langevin dynamics
Pietro Giudice, Gert Aarts, Erhard Seiler
Wed, 08:50, Seminar Room A -- Parallels 5A (Slides)

Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker-Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected.

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Inverse magnetic catalysis in QCD
Tamas G. Kovacs, Falk Bruckmann, Gergely Endrodi
Wed, 08:50, Seminar Room B -- Parallels 5B (Slides)

We propose a physical mechanism for inverse magnetic catalysis, the suppression of the chiral condensate by an external magnetic field in QCD around the critical temperature. We show that this effect, seen in lattice simulations, is a result of how the sea quarks react to the magnetic field. We find that the suppression of the condensate happens because the quark determinant can suppress low quark modes by ordering the Polyakov loop. This mechanism is particularly efficient around $$T_c$$ where the Polyakov loop effective potential is flat and the determinant can have a significant ordering effect. Our picture suggests that for the description of QCD in large magnetic fields it is crucial to properly capture the interaction between the Polyakov loop and the sea quarks, both in effective low-energy models and on the lattice.

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Towards Continuum Limit for the QCD Critical Point
Rajiv V. Gavai, Saumen Datta, Sourendu Gupta
Wed, 09:10, Seminar Room A -- Parallels 5A (Slides)

Results from our simulations of QCD with two light dynamical staggered flavours of mass $$m/T_c =0.1$$ are presented. Employing our earlier proposed Taylor series method for the baryonic susceptibility, we estimate the radius of convergence by using terms up to the eighth order susceptibility, $$\chi_8$$. Comparing with earlier results on coarser lattices, we find a very good agreement between the $$N_t = 8$$ and $$6$$ lattices for its location in the $$(\mu_B/T, T/T_c)$$ plane, suggesting any cut-off effects to be encouragingly small.

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Magnetization and pressures at nonzero magnetic fields in QCD
Gergely Endrodi, Gunnar Bali, Falk Bruckmann, Florian Gruber, Andreas Schaefer
Wed, 09:10, Seminar Room B -- Parallels 5B (Slides)

We study the influence of strong magnetic fields on gluonic and fermionic observables in QCD. The magnetic field is found to induce an anisotropy between certain components of the QCD action. We show that on a finite lattice - where the magnetic flux is quantized - this anisotropy is related to the difference of pressures in the directions parallel and perpendicular to the magnetic field. From the pressure anisotropy, the QCD magnetization is estimated, indicating that QCD is paramagnetic.

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Controlling errors in simulations for QCD at finite chemical potential
Sourendu Gupta, Saumen Datta, Rajiv V. Gavai
Wed, 09:30, Seminar Room A -- Parallels 5A (Slides)

The control of errors in quantities determined at finite chemical potential through the Taylor series expansion requires some new techniques. We discuss these techniques and the scaling of errors. We also discuss how critical slowing down manifests itself when the critical point is only accessible through an extrapolation.

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The quark-gluon plasma in an external magnetic field
Carleton DeTar, Doctor Ludmila Levkova
Wed, 09:30, Seminar Room B -- Parallels 5B (Slides)

We present results of an exploratory study of the effect of a strong magnetic field on the equation of state of high temperature strongly interacting matter. Working with conventional gauge field ensembles at zero magnetic field, we compute terms up to second order in a Taylor series expansion of the pressure as a function of the magnetic field.

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Finite size scaling for 3 and 4-flavor QCD with finite chemical potential
Shinji Takeda, Xiao-Yong Jin, Yoshinobu Kuramashi, Yoshifumi Nakamura, Akira Ukawa
Wed, 09:50, Seminar Room A -- Parallels 5A (Slides)

We present a finite size scaling study for 3 and 4-flavor QCD with nonzero quark chemical potential by the grand canonical approach. We employ the Wilson-clover fermions and adopt the phase reweighting method where the phase factor is computed exactly. In 4-flavor study, we show the finite size scaling study for the moments of various physical quantities, which demonstrates a typical behavior of the 1st order phase transition as well as the crossover or weak 1st order phase transition. For 3-flavor study, we try to identify the critical end point in the parameter space of the hopping parameter, the gauge coupling and the chemical potential.

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The magnetic susceptibility in QCD
Claudio Bonati, Massimo D'Elia, Marco Mariti, Francesco Negro, Francesco Sanfilippo
Wed, 09:50, Seminar Room B -- Parallels 5B (Slides)

Recently much work has been devoted to the study of QCD coupled to a background magnetic field. Quarks and gluons act as a magnetic medium and a natural question arises: is this medium paramagnetic or diamagnetic? Despite the simplicity of this question, it is non trivial to get an answer by means of LQCD simulations. We will review the technical difficulties related to this problem and present the results of our study.

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Results from combining ensembles at several values of chemical potential
Xiao-Yong Jin, Yoshinobu Kuramashi, Yoshifumi Nakamura, Shinji Takeda, Akira Ukawa
Wed, 10:10, Seminar Room A -- Parallels 5A (Slides)

We have been studying QCD with finite temperature and density for 3 and 4 degenerate quark flavors using the Wilson-clover action with a phase-quenched fermion determinant. Typically, with a fixed quark mass and a lattice coupling, we have a few ensembles at distinct values of chemical potentials scattered around the transition/cross-over region. Reweighting from ensembles simulated at multiple parameter values enables us to achieve higher statistics and a better sampling of the configuration space. We are able to obtain the information of partition functions at various parameter values, as well as complex-valued partition functions in the complex parameter space. In this talk, we discuss our careful approach to multi-ensemble reweighting, and present results mainly on zeros of partition functions in the complex parameter space.

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Electric charge catalysis by magnetic fields and a nontrivial holonomy
Tin Sulejmanpasic, Falk Bruckmann, Pavel Buividovich
Wed, 10:10, Seminar Room B -- Parallels 5B (Slides)

We describe a generic mechanism by which a system of Dirac fermions in thermal equilibrium acquires electric charge in an external magnetic field. To this end the fermions should have an additional quantum number, isospin or color, and should be subject to a second magnetic field, which distinguishes the isospin/color, as well as to a corresponding isospin chemical potential. The role of the latter can be also played by a nontrivial holonomy (Polyakov loop) along the Euclidean time direction. The charge is accumulated since the degeneracies of occupied lowest Landau levels for particles of positive isospin and anti-particles of negative isospin are different. We discuss two physical systems, where this phenomenon can be realized. One is monolayer graphene, where the isospin is associated with two valleys in the Brillouin zone and the strain-induced pseudo-magnetic field acts differently on charge carriers in different valleys. Another is hot QCD, for which the relevant non-Abelian field configurations with both nonzero chromo-magnetic field and a nontrivial Polyakov loop can be realized as calorons - topological solutions of Yang-Mills equations at finite temperature. The induced electric charge on the caloron field configuration is studied numerically. We argue that due to the fluctuations of holonomy external magnetic field should tend to suppress charge fluctuations in the quark-gluon plasma and estimate the importance of this effect for off-central heavy-ion collisions.

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Effective Polyakov line actions via the relative weights method
Jeff Greensite, Kurt Langfeld
Wed, 11:00, Seminar Room A -- Parallels 6A (Slides)

We apply a novel method to determine the effective Polyakov line action corresponding to an underlying lattice gauge theory. The effective theory is tested by comparing Polyakov line correlators computed in the effective theory and the lattice gauge theory, and these correlators are found to agree quite well. For pure SU(2) gauge theory, the effective action turns out to be bilinear in the Polyakov lines, while matter fields add a center symmetry-breaking linear term.

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Quark localization in QCD above $$T_c$$
Ferenc Pittler, Matteo Giordano, Tamas G. Kovacs
Wed, 11:00, Seminar Room B -- Parallels 6B (Slides)

It was previously found that at high temperature the lowest part of the QCD Dirac spectrum consists of localized modes obeying Poisson statistics. Higher up in the spectrum, modes become delocalized and their statistics can be described by random matrix theory. The transition from localized to delocalized modes is analogous to the Anderson metal-insulator transition. Here we use dynamical QCD simulations with staggered quarks to study this localization phenomenon. We show that the mobility edge, separating localized and delocalized modes, scales properly in the continuum limit and rises steeply with the temperature. Using very high statistics simulations in large volumes we find that the density of localized modes scales precisely with the spatial volume and even at $$T=2.6T_c$$ the lowest part of the spectrum extends all the way down to zero with no evidence of a spectral gap.

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Effective lattice theory for finite temperature Yang Mills
Georg Bergner, Jens Langelage, Owe Philipsen
Wed, 11:20, Seminar Room A -- Parallels 6A (Slides)

Effective Polyakov loop models are a useful tool for an investigation of pure Yang-Mills theory and full QCD. A systematic derivation of the effective action can be done in a strong coupling expansion. Quite accurate predictions for phase transition have been obtained in this approach. Further observables can be measured in the effective model. These provide additional tests for the reliability of the strong coupling approach and the truncation of the effective action. In this talk I will present recent results for these observables. In particular the free energy of the static quark-antiquark pair in the effective theory is compared with the results in full Yang-Mills theory.

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Critical behaviour in the QCD Anderson transition
Matteo Giordano, Ferenc Pittler, Tamas G. Kovacs
Wed, 11:20, Seminar Room B -- Parallels 6B (Slides)

We study the Anderson-type localisation-delocalisation transition found previously in the QCD Dirac spectrum at high temperature. Using high statistics QCD simulations with $$N_f=2+1$$ flavours of staggered quarks, we discuss how the change in the spectral statistics depends on the volume, the temperature and the lattice spacing, and we speculate on the possible universality of the transition from Poisson to Wigner-Dyson in the spectral statistics. Moreover, we show that the transition is a genuine phase transition: at the mobility edge, separating localised and delocalised modes, quantities characterising the spectral statistics become non-analytic in the thermodynamic limit. Using finite size scaling we also determine the critical exponent of the correlation length, and we speculate on possible extensions of the universality of Anderson transitions.

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Local Polyakov loop domains and their fractality
Hans-Peter Schadler, Christof Gattringer, Gergely Endrodi
Wed, 11:40, Seminar Room A -- Parallels 6A (Slides)

We discuss center cluster properties of the local Polyakov loop in SU(3) lattice gauge theory at finite temperature. These center clusters are defined by the phase of the local Polyakov loops in the vicinity of center elements of the gauge group. We perform the analysis in a fixed scale approach and study various properties of the center clusters, e.g., percolation probability or fractality. Results and physical implications for temperatures below and above the phase transition are discussed.

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Thermal field theories and shifted boundary conditions
Leonardo Giusti, Harvey Meyer
Wed, 11:40, Seminar Room B -- Parallels 6B (Slides)

The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L0 and the shift xi only through the combination $$\beta=L_0(1+\xi^2)^{1/2}$$. This in turn implies a set of Ward identities among the correlators of the energy-momentum tensor which have interesting applications in lattice field theory. In particular, they offer identities to renormalize non-perturbatively the energy-momentum tensor and novel ways to compute thermodynamic potentials. At fixed bare parameters they also provide a simple method to vary the temperature in much smaller steps than with the standard procedure.

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Deconfinement and theta dependence in SU(N) Yang-Mills theories
Francesco Negro, Claudio Bonati, Francesco Capponi, Massimo D'Elia
Wed, 12:00, Seminar Room A -- Parallels 6A (Slides)

We study the dependence of the deconfinement temperature on the theta parameter for SU(N) gauge theories, with N = 2, 3, 4. Results have been obtained for imaginary theta and analytically continued to real theta, in order to determine the curvature of the critical line $$T_c(\theta)$$. A comparison with reweighting at real theta is performed to check for the validity of analytic continuation. We also discuss some general features of the phase diagram in the T-theta plane and the dependence of physical observables on the topological sector around the transition.

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Finite temperature behaviour of glueballs in Lattice Gauge Theories
Roberto Pellegrini, Michele Caselle
Wed, 12:00, Seminar Room B -- Parallels 6B (Slides)

We propose a new method to compute glueball masses in finite temperature Lattice Gauge Theories which at low temperature is fully compatible with the known zero temperature results and as the temperature increases leads to a glueball spectrum which vanishes at the deconfinement transition. We show that this definition is consistent with the Isgur-Paton model and with the expected contribution of the glueball spectrum to various thermodynamic quantities at finite temperature. We test our proposal with a set of high precision numerical simulations in the 3d gauge Ising model and find a good agreement with our predictions.

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Theta dependence of 4D SU(N) gauge theories at finite temperature
Ettore Vicari, Claudio Bonati, Massimo D'Elia, Haralambos (Haris) Panagopoulos
Wed, 12:20, Seminar Room A -- Parallels 6A (Slides)

The dependence of 4D SU(N) gauge theories on the topological theta term is discussed at finite temperature, and in particular in the large-N limit. Theoretical arguments and numerical analyses exploiting the lattice formulation show that it drastically changes across the deconfinement transition. The low-T phase is characterized by a large-N scaling with theta/N as relevant variable, while in the high-T phase the scaling variable is just theta and the free energy is essentially determined by the instanton-gas approximation.

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Pursuing QCD Phase Transition with Lattice QCD and Experimental Data
Atsushi Nakamura, Keitaro Nagata
Wed, 12:20, Seminar Room B -- Parallels 6B (Slides)

Recent RHIC Beam Energy Scan opens an exciting opportunity for us working in numerical simulations. First, the freeze-out temperature and chemical potential are estimated by several phenomenological analyses. Secondly and very importantly, they provide the net-proton multiplicity at each incident energy. From the data, we can construct the canonical partition functions, $$Z_n$$, which are a link between experimental and numerical approaches assuming that the number conserves after the chemical freeze-out. Once we have the $$Z_n$$, we can calculate a grand canonical partition function, $$Z(\xi) = \sum_n Z_n \xi^n$$, where $$\xi=\exp(\mu/T)$$. On the contrary, we can calculate $$Z_n = \int {\rm d} \xi \exp(i\theta) Z(\theta)$$, where $$\theta=i \mu/T$$. Namely in lattice QCD, we can calculate $$Z_n$$ by integrating over the imaginary chemical potential where the fermion action is real. We show the Lee-Yang zero distributions both from experimental and lattice data, and compare them. The Lee-Yang zeros are fugacity ($$\exp(\mu/T)$$) points in the complex fugacity plane on which the grand partition function vanishes, $$Z(\xi)=0$$. We also report a novel method which allows u to get all the Lee-Yang zeros safely and reliably.

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Practical approach to the sign problem at finite theta-vacuum angle
Takahiro Sasaki, Hiroaki Kouno, Masanobu Yahiro
Wed, 12:40, Seminar Room A -- Parallels 6A (Slides)

We investigate a way of circumventing the sign problem in lattice QCD simulations with a theta-vacuum term, using the Polyakov-loop extended Nambu-Jona-Lasinio model. We consider the reweighting method for the QCD Lagrangian after the $$U_A(1)$$ transformation. In the Lagrangian, the P-odd mass term as a cause of the sign problem is minimized. In order to find a good reference system in the reweighting method, we estimate the average reweighting factor by using the two-flavor Polyakov-loop extended Nambu-Jona-Lasinio model and eventually find a good reference system.

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The critical endpoint of the finite temperature phase transition for three flavor QCD with clover type fermions
Yoshifumi Nakamura, Xiao-Yong Jin, Yoshinobu Kuramashi, Shinji Takeda, Akira Ukawa
Thu, 14:00, Seminar Room A -- Parallels 7A (Slides)

We investigate the critical endpoint of QCD at zero chemical potential. We employ the renormalization-group improved Iwasaki gluon action and both stout link smeared clover and non-smeared clover action with cSW determined non-perturbatively. The critical endpoint is determined by using the intersection points of the Binder cumulants at Lt=4, 6, 8 and extrapolated to the continuum limit.

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1st or 2nd; the order of finite temperature phase transition of $$N_f=2$$ QCD from effective theory analysis
Yusuke Taniguchi, Sinya Aoki, Hidenori Fukaya
Thu, 14:20, Seminar Room A -- Parallels 7A (Slides)

In the preceding study we showed the $$U(1)_A$$ symmetry is presumably recovered in the $$N_f=2$$ QCD at finite temperature $$T>T_c$$, where we used a fact that the $$SU(2)_L\times SU(2)_R$$ chiral symmetry is restored as an input and argued that every order parameter of the $$U(1)_A$$ symmetry made of (pseudo) scalar density vanishes if the thermodynamical limit is taken correctly. In this talk we use the low energy effective theory of the $$N_f=2$$ QCD and adopt the fact that order parameters of the $$U(1)_A$$ symmetry vanish as an input. We first argue that the effective theory recovers at least $$SU(2)_L \times SU(2)_R \times Z_8$$ symmetry at $$T>T_c$$, where $$Z_8$$ is a subgroup of $$U(1)_A$$, in order to eliminate the $$U(1)_A$$ order parameters. Then we perform the renormalization group analysis of the IR fixed point at one loop, for which we do not find any stable one. Our conclusion is that the order of the finite temperature phase transition seems to be 1st.

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Effective lattice theory for finite density QCD: derivation
Jens Langelage, Mathias Neuman, Owe Philipsen
Thu, 14:40, Seminar Room A -- Parallels 7A (Slides)

We discuss the derivation of the fermionic part of the dimensionally reduced effective action at small temperatures. The resulting expression is computed through three orders in a hopping parameter expansion and satisfies the Pauli principle. Afterwards we resum an infinite number of terms in order to improve convergence. Finally we remark on the inclusion of gauge corrections.

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Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks
Mathias Neuman, Jens Langelage, Stefano Lottini, Owe Philipsen
Thu, 15:00, Seminar Room A -- Parallels 7A (Slides)

In this talk we present the application of the complex Langevin algorithm to a three-dimensional effective lattice theory for heavy quarks. With this approach it is possible to avoid the sign problem and simulate the theory at all values of the baryon chemical potential. To confirm the correctness of the results, we check that the recently developed convergence criteria for Langevin simulations are met and compare with Monte Carlo data. Results for the onset transition to cold nuclear matter are presented.

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The Phase Diagram of Strong Coupling QCD including Gauge Corrections
Wolfgang Unger, Philippe de Forcrand, Owe Philipsen, Jens Langelage, Kohtaroh Miura
Thu, 15:20, Seminar Room A -- Parallels 7A (Slides)

The strong coupling limit of staggered lattice QCD has been studied since decades, both via Monte Carlo and mean field theory. In this model, the finite density sign problem is mild and the full phase diagram can be studied, even in the chiral limit. It is however desirable to understand the effect of a finite lattice gauge coupling beta on the phase diagram in the mu-T plane in order to see how it might be related to the phase diagram of continuum QCD. Here we discuss how to construct an effective theory for non-zero lattice coupling, valid to O(beta), and present Monte Carlo results incorporating these corrections, in particular for corrections to the chiral susceptibility and the baryon density.

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QCD phase diagram at strong coupling including auxiliary field fluctuations
Terukazu Ichihara, Akira Ohnishi, Takashi Z. Nakano
Thu, 15:40, Seminar Room A -- Parallels 7A (Slides)

We study the QCD phase diagram in the strong coupling lattice QCD by using an auxiliary field Monte-Carlo (AFMC) method, and search for a way to avoid the sign problem. In many of previous researches, the QCD phase diagram has been studied in the mean field approximation. Including fluctuation is now a theoretical challenge. However, we have the sign problem in both AFMC and the monomer-dimer-polymer (MDP) simulations. The sign problem is characterized by the difference of the free energy density, $$\epsilon_f$$, in full and quenched MC simulations. We realize $$\epsilon_f$$ in AFMC is about twice as large as that in MDP. This means that our method has more severe weight cancellation than MDP. We reveal that this cancellation is caused by high momentum auxiliary field components, and qualitatively confirm the effects of the high momentum auxiliary fields. This analysis shows a possibility that we could investigate phase transition phenomena on a large lattice by cutting off or by approximately integrating out the high momentum auxiliary fields. In the presentation, we will briefly mention the AFMC method and show the cut-off momentum dependence of the weight cancellation. We will also discuss the possibility of investigating the QCD phase diagram on a larger lattice.

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Susceptibilities in $$N_f=2$$ QCD
Saumen Datta, Rajiv V. Gavai, Sourendu Gupta
Thu, 16:30, Seminar Room A -- Parallels 8A (Slides)

We present results from our study of susceptibilities in QCD with two light flavors of quarks. Using $$N_t=8$$ lattices and staggered quark action, and quark masses such that the pion mass is about 220 MeV, we calculate susceptibilities, and use them to calculate the pressure and the baryon number susceptibility at small values of $$\mu_B$$, the baryon number chemical potential.

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QCD thermodynamics with O(a) improved Wilson fermions at $$N_f=2$$
Bastian Brandt, Anthony Francis, Harvey Meyer, Owe Philipsen, Hartmut Wittig
Thu, 16:50, Seminar Room A -- Parallels 8A (Slides)

We present an update of our study of the phase diagram of two-flavour QCD at zero density with dynamical $$O(a)$$-improved Wilson quarks. All simulations are done on lattices with a temporal extent of $$N_t=16$$ and spatial extent $$L=32,48$$ and 64, ensuring that discretisation effects are small and finite size effects can be controlled. In the approach to the chiral limit we currently have two scans along lines of constant physics at $$m_\pi=290$$ and 200 MeV. In addition to Polyakov loop and chiral condensate, we also measure spectroscopic observables, such as screening masses, to investigate the pattern of chiral symmetry restoration. Furthermore, we measure temporal correlation functions to extract information about spectral functions in confined and deconfined phases and to learn about plasma properties close to the critical temperature.

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Investigation of the $$U_A(1)$$ in high temperature QCD on the lattice
Sayantan Sharma, Viktor Dick, Frithjof Karsch, Edwin Laermann, Swagato Mukherjee
Thu, 17:10, Seminar Room A -- Parallels 8A (Slides)

In this project we study the effects of the $$U_A(1)$$ anomaly for 2+1-flavour QCD at high temperature. We apply the overlap operator as a tool to probe the topological properties of gauge field configurations which have been generated within the Highly Improved Staggered Quark (HISQ) discretization scheme on lattices of size $$32^3times 8$$ with $$m_l/m_s=1/20$$, commonly used for the study of QCD thermodynamics. Although we have at present, only results for one value of the quark masses and thus cannot monitor the change of the eigenvalue distributions with the light quark mass, the distribution of the low-lying eigenvalues of the overlap operator suggests that the $$U_A(1)$$ is not restored effectively even at 1.5 times the pseudo critical temperature. The corresponding low-lying eigenmodes show localization properties.

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QCD thermodynamics with dynamical overlap fermions
Balint Toth, Szabolcs Borsanyi, Ydalia Delgado Mercado, Stephan Durr, Zoltan Fodor, Sandor Katz, Stefan Krieg, Thomas Lippert, Dániel Nógrádi, Kálmán Szabó
Thu, 17:30, Seminar Room A -- Parallels 8A (Slides)

We extend our study of QCD thermodynamics using two flavors of dynamical overlap fermions to $$N_t=10$$ and $$N_t=12$$. We work in a fixed global topology setting with a quark mass corresponding to a pion mass of 350 MeV.

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Chiral symmetry and axial U(1) symmetry in finite temperature QCD with domain-wall fermion
Ting-Wai Chiu, Wen-Ping Chen, Yu-Chih Chen, Han-Yi Chou, Tung-Han Hsieh
Thu, 17:50, Seminar Room A -- Parallels 8A (Slides)

We study the restoration of the spontaneously broken chiral symmetry and the anomalously broken axial U(1) symmetry in finite temperature QCD at zero chemical potential. We use 2 flavors lattice QCD with optimal domain-wall fermion on the $$16^3 \times 6$$ lattice, with the extent $$N_s = 16$$ in the fifth dimension, in the temperature range $$T = 150-250$$ MeV. To examine the restoration of the chiral symmetry and the axial $$U(1)$$ symmetry, we use diluted $$Z_2$$ noises to calculate the chiral condensate, and the chiral susceptibilities in the scalar and pseudoscalar meson channels, for flavor singlet and non-singlet respectively. From the degeneracy of the chiral susceptibilities around $$T_c$$, it suggests that the axial $$U(1)$$ symmetry is restored in the chirally symmetric phase. Moreover, we examine the spectral density $$\rho(\lambda)$$ of the overlap Dirac operator, which is obtained by computing zero modes plus 400 low-lying modes for each gauge configuration. The existence of a gap in the spectral density around $$\lambda=0$$ for $$T \simeq T_c$$ provides a consistency check of the restoration of axial $$U(1)$$ symmetry in the chirally symmetric phase.

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The chiral phase transition of $$N_f=2$$ QCD at imaginary and zero chemical potential
Owe Philipsen, Claudio Bonati, Massimo D'Elia, Philippe de Forcrand, Francesco Sanfilippo
Thu, 18:10, Seminar Room A -- Parallels 8A (Slides)

The chiral symmetry of QCD with two massless quark flavours gets restored in a non-analytic chiral phase transition at finite temperature and zero density. Whether this is a first order or a second order transition with O(4) (or O(2)) universality has not yet been determined unambiguously, due to the difficulties of simulating light quarks. We investigate the nature of the chiral transition as a function of quark mass and imaginary chemical potential, using staggered fermions on $$N_t=4$$ lattices. At sufficiently large imaginary chemical potential, a clear signal for a first order transition is obtained for small masses, which weakens with decreasing imaginary chemical potential. The second order critical line $$m_c(\mu_i)$$, which marks the boundary between first order and crossover behaviour, extrapolates to a finite $$m_c(0)$$ with known critical exponents. This implies a definitely first order transition in the chiral limit on coarse lattices.

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Banks-Casher-type relations for complex Dirac spectra
Tilo Wettig, Takuya Kanazawa, Naoki Yamamoto
Fri, 14:00, Seminar Room A -- Parallels 9A (Slides)

For theories with a sign problem there is no analog of the Banks-Casher relation. This is true in particular for QCD at nonzero quark chemical potential. However, for QCD-like theories without a sign problem the Banks-Casher relation can be extended to the case of complex Dirac eigenvalues. We derive such extensions for the zero-temperature, high-density limits of two-color QCD, QCD at nonzero isospin chemical potential, and adjoint QCD. In all three cases the density of the complex Dirac eigenvalues at the origin is proportional to the BCS gap.

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Sign problem and subsets in one-dimensional QCD
Jacques Bloch, Falk Bruckmann, Tilo Wettig
Fri, 14:20, Seminar Room A -- Parallels 9A (Slides)

We present a subset method that solves the sign problem for QCD at nonzero quark chemical potential in 0+1 dimensions. The subsets of gauge configurations are constructed using the center symmetry of the SU(3) group. These subsets completely solve the sign problem for up to five flavors. For a larger number of flavors the sign problem slowly reappears and we propose an extension of the subsets that also solves the sign problem for these cases. The subset method allows for numerical simulations of the model at nonzero chemical potential.

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Extended Mean Field Study of Complex $$\phi^4$$-Theory at Finite Density and Temperature
Oscar Akerlund, Philippe de Forcrand
Fri, 14:40, Seminar Room A -- Parallels 9A (Slides)

We apply the Extended Mean Field (EMFT) approximation to complex, scalar $$\phi^4$$-theory. We determine the $$(T,\mu)$$ phase diagram and study the critical properties of the transition at zero and finite temperature. We are also able to determine finite volume corrections to the critical chemical potential $$\mu_c$$. We obtain results which agree very well with recent Monte Carlo studies both at zero and non-zero temperature. Within our approximation we do not suffer from finite volume effects and can thus obtain results at lattice spacings unobtainable by present Monte Carlo simulations. We find that our approximation reproduces many phenomena of the exact model like the Silver Blaze'' behaviour at zero temperature and dimensional reduction at finite temperature. At finite temperature we find a weak first order transition where the expectation value of the field jumps proportionally to the temperature. Due to a jump in the free energy at the transition we conclude that this is caused by a failure of the approximation and should not be ascribed any physical meaning. It seems plausible that this pathology could be fixed by keeping more terms in the effective action.

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The Lefschetz thimble and the sign problem
Luigi Scorzato
Fri, 15:00, Seminar Room A -- Parallels 9A (Slides)

I introduce the "Lefschetz thimble" and explain how it can be used to perform Monte Carlo simulations of lattice quantum field theories (QFT) with a sign problem. The formulation of a QFT on the Lefschetz thimble does not coincide with the traditional formulation, exactly, but it is a legitimate, alternative regularization, on the basis of universality. In fact, I analyze the symmetries and the perturbative expansion of the new formulation. I also describe the algorithm that we proposed to sample the configurations from the thimble. A great advantage of this approach is its rather general applicability. In particular, I show that it is applicable, in principle, also to QCD at finite density.

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Relativistic Bose gas on a Lefschetz thimble
Marco Cristoforetti
Fri, 15:20, Seminar Room A -- Parallels 9A (Slides)

We study on the lattice a complex relativistic scalar field with quartic interaction. In this theory, as in QCD, the sign problem prevents the use of Monte Carlo methods for the study of phenomena emerging at finite chemical potential, such as the Silver Blaze problem. Integrating the complex extension of the partition function on Letschetz thimbles we will show that the sign problem can be solved and Silver Blaze phenomenon are well reproduced.

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Towards a density of states approach for dense matter systems
Kurt Langfeld, Biagio Lucini, Antonio Rago, Jan Pawlowski, Roberto Pellegrini
Fri, 15:40, Seminar Room A -- Parallels 9A (Slides)

The density-of-states method (Phys.Rev.Lett. 109 (2012) 111601) features an exponential error suppression and is not restricted to theories with positive probabilistic weight. It is applied to the SU(2) gauge theory at finite densities of heavy quarks. Key ingredient here is the Polyakov line probability distribution, which is obtained of over 80 orders of magnitude. We briefly address whether the exponential error suppression could be sufficient to simulate theories with a strong sign problem.

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Heavy quark potential at finite imaginary chemical potential
Junichi Takahashi, Takahiro Sasaki, Keitaro Nagata, Takuya Saito, Hiroaki Kouno, Masanobu Yahiro, Atsushi Nakamura
Fri, 16:30, Seminar Room A -- Parallels 10A (Slides)

We study the heavy quark potential at finite temperature and chemical potential by lattice QCD, using the Polyakov loop correlation function. We use a renormalization group improved gluon action and a clover-improved Wilson quark action of two flavors and perform the simulation on a $$16^3\times 4$$ lattice. So far, the heavy quark potential has been studied mainly at zero chemical potential, because the quark determinant is complex at finite chemical potential. We calculate the heavy quark potential in various color channels at imaginary chemical potential where there is no sign problem. Moreover, we calculate Taylor expansion coefficients of the heavy quark potential up to forth order at imaginary chemical potential. Particularly, in the color-singlet and color-octet channels, we change the sign of the second order coefficient of the Taylor expansion in order to obtain the heavy quark potential at real chemical potential from that at imaginary chemical potential. In the color-sextet and color-anti-triplet channels, the heavy quark potential become complex at imaginary chemical potential, because the heavy quark potential is not invariant under the charge conjugation.However, this complex heavy quark potential become real at real chemical potential after the extrapolation from imaginary chemical potential to real chemical potential. We also discuss chemical potential dependence of color screening mass.

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G2-QCD: Spectroscopy and the phase diagram at zero temperature and finite density
Björn Wellegehausen, Axel Maas, Andreas Wipf, Lorenz von Smekal
Fri, 16:30, Seminar Room B -- Parallels 10B (Slides)

G2-QCD is a QCD-like theory with fermionic baryons and fundamental quarks. Unlike QCD it does not suffer from a fermionic sign problem at finite baryon density and therefore allows to investigate effects of fermionic baryons on the G2-QCD phase diagram with standard Monte-Carlo methods. In the talk our latest results on mass spectroscopy and the phase diagram at zero temperature and finite baryon density are presented.

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P wave bottomonium spectral functions in the QGP from lattice NRQCD
Gert Aarts, Chris Allton, Jon-Ivar Skullerud, Sinead Ryan, Donald Sinclair, Seyong Kim, Maria Paola Lombardo
Fri, 16:50, Seminar Room A -- Parallels 10A (Slides)

The melting pattern of bottomonium states in the quark-gluon plasma can provide information on the temperatures reached in heavy-ion collisions. Here results in the P wave channel, using NRQCD on a two-flavour background, are presented. We use the Maximum Entropy Method to construct spectral functions and pay attention to the stability under variation of input parameters.

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SO(2N) and SU(N) gauge theories
Richard Lau, Michael Teper
Fri, 16:50, Seminar Room B -- Parallels 10B (Slides)

We present our initial results of SO(2N) gauge theories, approaching the large-N limit. SO(2N) theories may help us to understand QCD at finite chemical potential since there is an orbifold equivalence between SO(2N) and SU(N) gauge theories at large N and SO(2N) theories do not have the sign problem present in QCD. We consider the mass spectra, string tensions, and deconfinement temperatures in the SO(2N) pure gauge theories in 2+1 dimensions, comparing them to their corresponding SU(N) theories.

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Charmonium Potentials at Non-Zero Temperature
Wynne Evans, Chris Allton, Pietro Giudice, Jon-Ivar Skullerud
Fri, 17:10, Seminar Room A -- Parallels 10A (Slides)

Inter-quark potentials from lattice QCD aid experimental investigations and improve the theoretical picture surrounding heavy quarkonia suppression. In this work, the charmonium potential is calculated using the HAL QCD method developed for nucleon-nucleon potentials. This requires correlators of extended charmonium operators as input. S-wave charmonium potentials are calculated at temperatures between 145MeV and 290MeV using 2+1 light dynamical quarks on anisotropic lattices. Results show a clear temperature dependence consistent with the expectation that the potential should become de-confining at high temperatures.

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Staggered operator with topological SU(2) backgrounds at nonzero chemical potential
Rudolf Rödl, Falk Bruckmann, Tin Sulejmanpasic
Fri, 17:10, Seminar Room B -- Parallels 10B (Slides)

We present zero modes of topological SU(2) backgrounds at nonzero chemical potential and temperature through the staggered operator. The latter possesses quartet quasi-zero modes, the profiles of which agree very well with continuum zero mode profiles (known analytically). These modes exhibit stronger peaks at the core and negative regions in their densities.

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Lattice NRQCD study of in-medium bottomonium states using $$N_f = 2+1, 48^3 \times 12$$ HotQCD configurations
Seyong Kim, Peter Petreczky, Alexander Rothkopf
Fri, 17:30, Seminar Room A -- Parallels 10A (Slides)

The behavior of bottomonium state correlators at non-zero temperature, $$140.4 (\beta = 6.664) \ge T \ge 221 (\beta = 7.280)$$ (MeV), where the transition temperature is $$154(9)$$ (MeV), is studied, using lattice NRQCD on $$48^3 \times 12$$ HotQCD HiSQ configurations with light dynamical $$N_f = 2 + 1$$ ($$m_l/m_s = 0.05$$) staggered quarks. In order to understand finite temperature effects on quarkonium states, zero temperature behavior of bottomonium correlators is compared based on $$32^4$$ ($$\beta = 6.664, 6.800$$ and $$6.950$$) and $$48^3 \times 64$$ ($$\beta = 7.280)$$ lattices. We find that temperature effects on S-wave bottomonium states are small but P-wave bottomonium states show a noticeable temperature dependence above the transition temperaure.

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Phase transitions in dense 2-colour QCD
Jon-Ivar Skullerud, Tamer Boz, Seamus Cotter, Leonard Fister
Fri, 17:30, Seminar Room B -- Parallels 10B (Slides)

We investigate 2-colour QCD with 2 flavours of Wilson fermion at nonzero temperature T and quark chemical potential mu, with a pion mass of 700 MeV ($$m_\pi/m_\rho=0.8$$). From temperature scans at fixed mu we find that the critical temperature for the superfluid to normal transition depends only very weakly on mu above the onset chemical potential, while the deconfinement crossover temperature is clearly decreasing with mu. We find indications of a region of superfluid but deconfined matter at high mu and intermediate T. We also present results for the Landau-gauge gluon propagator in the hot and dense medium.

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Spectral functions of charmonium from 2 flavour anisotropic lattice data
Aoife Kelly, Jon-Ivar Skullerud, Dhagash Mehta, Bugra Oktay, Chris Allton
Fri, 17:50, Seminar Room A -- Parallels 10A (Slides)

The spectral functions of QCD can give us insight into properties of hadrons, and they are useful in probing the QCD vacuum. I will discuss the correlators and spectral functions of charmonium in high temperature 2 flavour QCD. The spectral functions have been obtained using the Maximum Entropy Method from anisotropic lattice data.

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Analytic continuation in two color QCD with clover-improved Wilson fermion at finite density
Yuji Sakai, Atsushi Nakamura
Fri, 17:50, Seminar Room B -- Parallels 10B (Slides)

We test the method of analytic continuation from imaginary to real chemical potential in two-color QCD, which is free from the sign problem. We employ a clover-improved Wilson fermion action of two-flavors and a renormalization-group improved gauge action. In particular, we consider the analytic continuation of the critical line, the quark number density and meson correlations.

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Bottomonium spectrum at finite temperature
Tim Harris, Gert Aarts, Chris Allton, Seyong Kim, Jon-Ivar Skullerud, Maria Paola Lombardo, Sinead Ryan
Fri, 18:10, Seminar Room A -- Parallels 10A (Slides)

I will present some updated results from the FASTSUM collaboration on the bottomonium spectrum at finite temperature. In this work we use new ensembles of anisotropic gauge configurations with 2+1 flavours of dynamical Wilson clover quark. The heavy valence quarks are treated using an improved NRQCD action. The behaviour of the S- and P-wave correlators above and below $$T_c$$ will be discussed. I will also include some preliminary results of the bottomonium spectral functions at finite temperature obtained using the maximum entropy method.

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Chiral restoration and deconfinement in two-color QCD with two flavors of staggered quarks
David Scheffler, Christian Schmidt, Dominik Smith, Lorenz von Smekal
Fri, 18:10, Seminar Room B -- Parallels 10B (Slides)

In preparation of lattice studies of the two-color QCD phase diagram we study chiral restoration and deconfinement at finite temperature with two flavors of staggered quarks using a RHMC algorithm on GPUs. We first present the chiral condensate, the Polyakov loop and corresponding susceptibilities. Using Ferrenberg-Swendsen reweighting we extract the maxima of the chiral susceptibility. We determine pseudo-critical couplings on various lattices with a chiral extrapolation in order to fix the relation between coupling and temperature. From the Polyakov loop distributions we obtain the constraint Polyakov loop potentials and via a Legendre transformation the effective Polyakov loop potential.

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Quarkonium correlation functions at finite temperature in the charm to bottom region
Hiroshi Ono
Fri, 18:30, Seminar Room A -- Parallels 10A (Slides)

Quarkonium correlation functions at finite temperature are studied in a region of the quark mass for charmonia to bottomonia in quenched lattice QCD with $$O(a)$$-improved Wilson quarks. Our simulations are performed on large isotropic lattices at temperatures in the range from about 0.75$$T_c$$ to 1.5$$T_c$$. We discuss temperature dependence as well as quark mass dependence of the quarkonium correlation functions at both vanishing and finite momenta.

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Determination of Karsch Coefficients for 2-colour QCD
Seamus Cotter, Pietro Giudice, Simon Hands, Jon-Ivar Skullerud
Fri, 18:30, Seminar Room B -- Parallels 10B (Slides)

We calculate the Karsch Coefficients with 2 flavours of Wilson fermion in 2-colour QCD. This is done by measuring four observables, namely the lattice spacing using the static quark potential, the mass ratio and fermion anisotropy using the meson dispersion, and the gluon anisotropy using the sideways potential. The resulting numbers can be then be used by means of a 4-dimensional fit to give the Karsch Coefficients. These are then used to renormalise the energy density in the quark and gluon sectors.

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Temporal mesonic correlators at NLO for any quark mass
Yannis Burnier, Mikko Laine
Fri, 18:50, Seminar Room A -- Parallels 10A (Slides)

Charm quarks play an intriguing role in quark-gluon plasma physics, being neither light nor so heavy that they could be trivially decoupled. We present NLO perturbative results for temporal mesonic correlators in various quantum number channels as a function of the quark mass. The physics associated with these correlators includes charm quark transport and charmonium bound state properties. We discuss the renormalization of the different channels, compare our perturbative results with quenched data from fine lattices, and determine the resolution that needs to be achieved if non-perturbative charm and charmonium properties are to be reliably extracted from numerical measurements.

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Taylor- and fugacity expansion for the effective center model of QCD at finite density
Poster Session

QCD suffers from the complex action problem as soon as a chemical potential is introduced and has therefore not been treated successfully yet in Monte Carlo simulations. A promising way to avoid the complex action problem is to introduce new degrees of freedom, where an exact transformation to so called dual variables results in a partition sum which has only real and positive contributions and allows for the application of Monte Carlo techniques. In this manner, for some effective theories of QCD the complex action problem has already been solved. One of those theories is the effective center model for which the two main expansion techniques used in QCD, Taylor and fugacity expansion, are compared to the results of simulations in terms of dual variables in order to assess the quality of the perturbative approaches and to improve these techniques for applications in QCD.

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Adaptive gauge cooling for complex Langevin dynamics
Lorenzo Bongiovanni, Gert Aarts, Ion-Olimpiu Stamatescu , Erhard Seiler, Denes Sexty
Poster Session

In the case of non abelian gauge theories with a complex weight, a controlled exploration of the complexified configuration space during a complex Langevin process requires the use of SL(N;C) gauge cooling, in order to minimize the distance from SU(N) . Here we show that adaptive gauge cooling can lead to an efficient implementation of this idea.

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Scaling properties of the chiral phase transition in the low density region of two-flavor QCD with improved Wilson fermions
Takashi Umeda, Sinya Aoki, Shinji Ejiri, Tetsuo Hatsuda, Kazuyuki Kanaya, Yu Maezawa, Yoshiyuki Nakagawa, Hiroshi Ono, Hana Saito, Shinsuke Yoshida
Poster Session

We study scaling behavior of a chiral order parameter in the low density region, performing a simulation of two-flavor QCD with improved Wilson quarks. The scaling behavior of the chiral order parameter defined by a Ward-Takahashi identity agrees with the scaling function of the three-dimensional O(4) spin model at zero chemical potential. We extend the scaling study to finite density QCD. Applying the reweighting method and calculating derivatives of the chiral order parameter with respect to the chemical potential, the scaling properties of the chiral phase transition are discussed in the low density region. We moreover calculate the curvature of the phase boundary of the chiral phase transition in the temperature and chemical potential plane assuming the O(4) scaling relation.

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Complex Langevin simulation for QCD-like models
Ion-Olimpiu Stamatescu, Gert Aarts, Lorenzo Bongiovanni, Jan Pawlowski, Erhard Seiler, Denes Sexty, Denes Sexty, Erhard Seiler
Poster Session

For theories with complex action, in particular QCD at non-zero density, the complex Langevin equation provides a unique simulation method. Its development and control is followed on some models of increasing complexity, for which some benchmark results are known by explicite calculations or by other methods. The methods shows in particular its capabilities in QCD with heavy quarks and full Yang-Mills action.

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A test of fugacity-, Taylor- and improved Taylor-expansion
Max Wilfling, Christof Gattringer
Poster Session

We compare three different expansion methods for observables as a function of the chemical potential using free fermions as a first test case. In addition to the conventional Taylor series, we analyze fugacity expansion, which is a finite Laurent series in the fugacity parameter with expansion coefficients that are canonical determinants for a fixed net quark number. We furthermore suggest an improved Taylor series which captures aspects of both the conventional Taylor series and the fugacity expansion. Convergence and other properties are compared for the three series.

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Towards the Continuum Limit in Transport Coefficient Computations
Thomas Neuhaus, Anthony Francis, Olaf Kaczmarek, Mikko Laine, Marcel Müller, Hiroshi Ono
Poster Session

The analytic continuation necessary for the extraction of transport coefficients is well-defined even in principle only when a continuous function of the Euclidean time variable is available. We report progress towards achieving the continuum limit for 2-point correlator measurements in pure SU(3) gauge theory, with specific attention paid to scale setting. As an application the determination of the heavy quark momentum diffusion coefficient from a correlator of colour-electric fields attached to a Polyakov loop is discussed.

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Landau gauge gluon and ghost propagators from two-flavour lattice QCD at nonzero temperature
Michael Muller-Preussker, Rafik Aouane, Florian Burger, Ernst-Michael Ilgenfritz, Andre Sternbeck
Poster Session

The temperature dependence of Landau gauge gluon and ghost propagators is studied in lattice QCD with two flavours of maximally twisted mass fermions within the crossover range. We present and analyze data which correspond to pion mass values between 300 and 500 MeV and also compare them with our previous $$N_f=0$$ results. For momenta between 0.4 and 3.0 GeV we are able to provide parametrizations of the lattice data which may serve as input for continuum functional methods, for example, for studies on the QCD phase diagram using Dyson-Schwinger equations.

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Finite coupling and fluctuation effects on the QCD phase diagram at strong coupling
Akira Ohnishi, Terukazu Ichihara, Takashi Z. Nakano
Poster Session

QCD at finite baryon density is one of the largest theoretical challenges in subatomic physics. While the lattice QCD Monte-Carlo simulations are successful at low densities, it is not yet possible to obtain reliable results for cold dense matter due to the sign problem. Strong coupling lattice QCD is one of the promising methods at finite density. We first integrate out spatial link variables analytically at a given order of the inverse coupling, then the statistical weight cancellation is reduced. Following the pioneering works in the mean field treatment [1], fluctuation effects are recently taken into account [2,3]. The next challenge is to include both finite coupling and fluctuation effects. We develop a framework to include the fluctuation and Polyakov loop effects. We combine the Haar measure method of the Polyakov loop [4] and the auxiliary field Monte-Carlo method of fluctuation [3]. In the presentation, we discuss how we can combine these two, and we will show some numerical results. [1] H. Kluberg-Stern et al.,Nucl. Phys. B190(1981)504; N. Kawamoto and J. Smit, Nucl. Phys. B 192, 100 (1981). [2] F. Karsch and K. H. Mutter, Nucl. Phys. B 313, 541 (1989); P. de Forcrand and M. Fromm, Phys. Rev. Lett. 104, 112005 (2010); W. Unger and P. de Forcrand, J. Phys. G 38, 124190 (2011). [3] A. Ohnishi, T. Ichihara, T. Z. Nakano, PoS LATTICE 2012 (2012), 088. [4] T. Z. Nakano, K. Miura, A. Ohnishi, Phys. Rev. D 83 (2011), 016014.

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Systematic Effects at Criticality for the SU(2)-Landau-Gauge Gluon Propagator
Tereza Mendes, Attilio Cucchieri
Poster Session

We analyze data from finite-temperature simulations of the gluon propagator in SU(2) Landau gauge on large lattices. We argue that the singular behavior seen previously in several studies of this quantity around the deconfinement transition is a lattice artifact.

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Finite-Temperature Spectral Functions from the Functional Renormalization Group
Ralf-Arno Tripolt, Nils Strodthoff, Lorenz von Smekal, Jochen Wambach
Poster Session

The computation of real-time observables represents a common challenge within lattice calculations and other Euclidean frameworks, where analytical continuation methods are needed to obtain results in Minkowski space-time. We present a method to obtain real-time 2-point functions and spectral functions for finite temperatures within the functional renormalization group approach. Here, the analytical continuation is done on the level of the flow equations in contrast to a continuation of the Euclidean data by, e.g., the maximum-entropy-method. Results are shown for the mesonic spectral functions in the quark-meson model at finite temperatures. Different in-medium processes affecting the mesonic spectral functions as well as effects of chiral symmetry restoration are discussed. An extension of this approach towards finite chemical potential and non-zero external spatial momenta will allow us to study critical regions of the phase diagram as well as transport coefficients.

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Measuring the entropy from shifted boundary conditions
Leonardo Giusti, Michele Pepe
Poster Session

We present preliminary results for the equation of state of the SU(3) Yang-Mills theory. In this study we consider the recent proposal of shifting the boundary conditions along the temporal direction to change the temperature of a relativistic quantum system. We perform an accurate investigation of the lattice artifacts in order to extract precise measurements in the continuum limit for a wide range of temperature values, while keeping finite size effects always under control.

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A new Bayesian approach to the reconstruction of spectral functions
Alexander Rothkopf, Yannis Burnier
Poster Session

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function $$m(\omega)$$ only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter $$\alpha$$ in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of $$P[\rho|D]$$ in the full $$N_\omega\gg N_\tau$$ dimensional search space. Several spectra are presented, which are reconstructed from realistic mock-data, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

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Benchmarking the Bayesian reconstruction of the non-perturbative heavy $$Q\bar{Q}$$ potential
Yannis Burnier, Alexander Rothkopf
Poster Session

The finite temperature complex heavy quark potential can be extracted form a spectral analysis of the lattice QCD Wilson loop. We benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. Namely we calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying spectral peak we obtain the real- and imaginary part and confirm that the knowledge of the lowest peak alone is sufficient. We then deploy a novel Bayesian approach for the reconstruction of spectral functions from the HTL Euclidean correlators and observe how well the known spectral function and values for the real and imaginary part are reproduced. Finally we apply the method to quenched lattice QCD data and perform an improved estimate of both real and imaginary part of the non-perturbative heavy $$Q\bar{Q}$$ potential.

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Electric charge susceptibility in 2+1 flavour QCD on an anisotropic lattice
Pietro Giudice, Gert Aarts, Chris Allton, Alessandro Amato, Simon Hands, Jon-Ivar Skullerud
Poster Session

We present our first results of the electic charge susceptibility in QCD using 2+1 dynamical quark flavours of Wilson quarks on anisotropic lattices. Spatial volumes of $$24^3$$ are used at fixed cut-off with temperatures ranging from $$T_c$$ and 2$$T_c$$.

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