# Applications Beyond QCD

In memory of Mikhail Igorevich Polikarpov
Wed, 08:30, Seminar Room E -- Parallels 5E (Slides)

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Monte-Carlo study of the semimetal-insulator phase transition in monolayer graphene with realistic inter-electron interaction potential
Maksim Ulybyshev
Wed, 08:50, Seminar Room E -- Parallels 5E (Slides)

The results of the first-principle numerical study of spontaneous breaking of chiral (sublattice) symmetry in monolayer graphene due to electrostatic interaction are presented. The screening of Coulomb potential by electrons on ?-orbitals is taken into account. It's found that suspended graphene is in the conducting phase with unbroken chiral symmetry, in contrast to the results of previous numerical simulations with unscreened potential. This finding is in agreement with recent experimental results by the Manchester group. Further, by artificially increasing the interaction strength we demonstrate that suspended graphene is quite close to the phase transition associated with spontaneous chiral symmetry breaking, which suggests that fluctuations of chirality and nonperturbative effects might still be quite important.

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Interaction of static charges in graphene within Monte-Carlo simulation
Victor Braguta, Semen Valgushev, Alexander Nikolaev, Mikhail Polikarpov, Maxim Ulybyshev
Wed, 09:10, Seminar Room E -- Parallels 5E (Slides)

The study of the interaction potential between static charges within Monte-Carlo simulation of graphene is carried out. The numerical simulations are performed in the effective lattice field theory with noncompact 3 + 1-dimensional Abelian lattice gauge fields and 2 + 1-dimensional staggered lattice fermions. At low temperature the interaction is well described by the Coulomb potential reduced by some dielectric permittivity R . The dependence of the R on the dielectric permittivity of substrate is determined. In addition, the renormalization of the quasiparticle charge is studied. At large temperatures the interaction potential is well described by the two dimensional Debye screening. The dependence of Debye screening mass on the dielectric permivitity of substrate allows to determine the position of the insulator-semimetal phase transition. It is shown that in the semimetal phase graphene reveals the properties of the two-dimensional plasma of fermions excitations.

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Lattice version of effective graphene field theory in terms of occupation numbers
Oleg Pavlovsky, Anna Sinelnikova, Maksim Ulybyshev
Wed, 09:30, Seminar Room E -- Parallels 5E (Slides)

Lattice version of effective graphene field theory in terms of occupation numbers will discussed. Phase transitions this theory will studied.

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Tight-binding model of graphene with Coulomb interactions
Dominik Smith, Lorenz von Smekal
Wed, 09:50, Seminar Room E -- Parallels 5E (Slides)

We present first results of HMC simulations of the tight-binding model of graphene with electron-electron interactions, based on the framework of Brower, Rebbi and Schaich. Interactions are modelled by an instantaneous long-range Coulomb potential, which is expressed as a Hubbard-Stratonovich field. We show that sub-lattice symmetry can be spontaneously broken, which corresponds to a phase transition to an insulating phase. We compare the discretization effects of simple and improved discretization schemes. Our goal is to investigate the effect of electronic interactions on the Lifshitz phase transition, associated with the Van Hove singularity around the saddle point in the dispersion relation, which is known to occur in the pure tight-binding model.

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Quantum Critical Behavior with massless Staggered fermions in Three Dimensions
Shailesh Chandrasekharan
Wed, 10:10, Seminar Room E -- Parallels 5E (Slides)

We use the fermion bag approach to study a variety of quantum critical behavior with massless staggered fermions in three dimensions. First, with one flavor of massless staggered fermions we show that lattice Gross-Neveu models and lattice Thirring models have the same critical exponents. Second, we study a $$Z_2$$ phase transition with one flavor of massless staggered fermions which could not be studied earlier due to sign problems and extract the critical exponents. Based on this we argue that results from a previous work may be misleading. Finally, we argue that with two flavors of staggered fermions and a specific type of four-fermion interaction, a surprising phase transition to a massive fermion phase without any spontaneous symmetry breaking may occur.

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Phase structure of topological insulators by lattice strong-coupling expansion
Yasufumi Araki, Taro Kimura
Wed, 11:00, Seminar Room E -- Parallels 6E (Slides)

The phase structure of topological insulators under a sufficiently strong electron-electron interaction is investigated. Topological insulators are materials with gapless surface states topologically protected by the time-reversal symmetry. The effective theory of topological insulators can be established on honeycomb of square lattices in terms of the Wilson fermion. Here we incorporate the effect of the electron-electron interaction in terms of U(1) lattice gauge theory (quantum electrodynamics), and analyze the phase structure by the techniques of strong coupling expansion. As a result, the phase structure is modified from that in the non-interacting limit. In 2-dimensional topological insulators, a sufficiently strong electron-electron interaction leads to the in-plane (tilted) antiferromagnetism, which possesses a similar structure to the well-known Aoki phase'' in lattice QCD with the Wilson fermion. We will also consider the phase structure of 3-dimensional topological insulators, and mention some physical implications about the experimental behavior of the materials.

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Topological Lattice Actions
Wolfgang Bietenholz, Michael Bögli, Urs Gerber, Ferenc Niedermayer, Michele Pepe, Fernando Rejón-Barrera, Uwe-Jens Wiese
Wed, 11:20, Seminar Room E -- Parallels 6E (Slides)

A variety of lattice discretizations of continuum actions has been considered in the literature, usually requiring the correct classical continuum limit. Here we discuss weird'' lattice formulation without that property, namely lattice actions that are invariant under small deformations of the field configuration, in one cases even without any couplings. It turns out that universality is powerful enough to still provide the correct quantum continuum limit, despite the absence of any classical limit, or a perturbative expansion. We demonstrate this for a set of non-linear sigma-models. Amazingly, such weird'' lattice actions even have practical benefits, in particular an excellent scaling behavior.

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MCRG Flow for the Nonlinear Sigma Model
Daniel Körner, Raphael Flore, Björn Wellegehausen, Andreas Wipf
Wed, 11:40, Seminar Room E -- Parallels 6E (Slides)

A study of the renormalization group flow in the three-dimensional nonlinear O(N) sigma model using Monte Carlo Renormalization Group (MCRG) techniques is presented. To achieve this, we combine an improved blockspin transformation with the canonical demon method to determine the flow diagram for a number of different truncations. Systematic errors of the approach are highlighted. Results are dis- cussed with hindsight on the fixed point structure of the model and the corresponding critical exponents. Special emphasis is drawn on the existence of a nontrivial ultraviolet fixed point which is a desired property for theories modeling the asymptotic safety scenario of quantum gravity.

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The gradient flow in a twisted box
Alberto Ramos
Wed, 12:00, Seminar Room E -- Parallels 6E (Slides)

We study the perturbative behavior of the gradient flow in a twisted box. We apply this information first to define a running coupling using the energy density of the flow field and to study the size of cutoff effects to leading order in perturbation theory. Second, we study the step scaling function and the size of cutoff effects in SU(2) pure gauge theory. We finally comment on how the gradient flow can be used to improve other running coupling definitions.

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Lattice Monte Carlo methods for systems far from equilibrium
David Mesterhazy, Luca Biferale, Karl Jansen, Raffaele Tripiccione
Wed, 12:20, Seminar Room E -- Parallels 6E (Slides)

We present a new numerical Monte Carlo approach to determine the scaling behavior of lattice field theories far from equilibrium. The presented methods are generally applicable to systems where classical-statistical fluctuations dominate the dynamics. As an example, these methods are applied to the random-force-driven one-dimensional Burgers' equation -- a model for hydrodynamic turbulence. For a self-similar forcing acting on all scales the system is driven to a nonequilibrium steady state characterized by a Kolmogorov energy spectrum. We extract correlation functions of single- and multi-point quantities and determine their scaling spectrum displaying anomalous scaling for high-order moments. Varying the external forcing we are able to tune the system continuously from equilibrium, where the fluctuations are short-range correlated, to the case where the system is strongly driven in the infrared. In the latter case the nonequilibrium scaling of small-scale fluctuations are shown to be universal.

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Hydrodynamics as a Quantum Field Theory on the lattice
Giorgio Torrieri, Tommy Burch
Wed, 12:40, Seminar Room E -- Parallels 6E (Slides)

As was known for some time, ideal hydrodynamics can be written as a field theory, suitable for quantization via the Feynman prescription [1]. Examining the fully quantum structure of ideal hydrodynamics can yield novel physical insights, including a "new way of thinking" about microscopic versus macroscopic dynamics and, perhaps, a new "quantum bound" for the viscosity over entropy density [2]. However, it is also clear that the quantum structure of this theory is highly non-perturbative [1,2]. In this work, we present our first effort to study ideal hydrodynamics as a field theory on the lattice. We will give an overview of the issues inherent in this analysis, define physically interesting observables, and present preliminary results, concentrating on averages of the scalar and tensor part of the energy momentum tensor of the ideal quantum fluid. [1] S.~Endlich, A.~Nicolis, R.~Rattazzi and J.~Wang, JHEP 1104, 102 (2011) [2] G. Torrieri, Phys.Rev. D85 (2012) 065006

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The unitary Fermi gas on the lattice
Olga Goulko, Matthew Wingate
Poster Session

Many interesting problems in the field of cold atoms cannot be solved analytically and require a numerical treatment. A prominent example is the resonantly interacting Fermi gas. In such cases lattice field theory is a very useful tool, since it allows first principles calculations without uncontrolled assumptions. One of the major challenges of the method is to extract the physical quantities in continuum and for an infinite system size from discrete data obtained for finite systems. I will discuss different methods and error sources on the example of the unitary Fermi gas at temperatures beyond the critical point.

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Large $$N$$ reduction in deformed Yang-Mills theories
Helvio Vairinhos
Poster Session

We explore, at the nonperturbative level, the large $$N$$ equivalence between ordinary $$SU(N)$$ Yang-Mills (YM) theory on $$\mathbb R^4$$, and $$SU(N)$$ YM theory on $$\mathbb R^3 \times S^1$$ with double-trace deformations. In particular, we compare the values of the $$0^{++}$$ glueball mass obtained in both sides of the equivalence.

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More about vacuum structure of Linear Sigma Model
Poster Session

We analytically study two aspects of $$U(N_f) \times U(N_f)$$ Linear sigma model (LSM). The first one is related to the effective restoration of $$U_A(1)$$ symmetry. Motivated by recent lattice data suggesting that two-flavor QCD may not obey O(4)-scaling, we study the effect of anomaly to the order of chiral phase transition in U(2) x U(2) LSM. The analysis is carried out in epsilon-expansion with a mass dependent renormalization scheme. We derive the condition that the model experiences the first order phase transition. The motivation of the second part is concerning lattice simulations of many flavor QCD using Wilson fermions. To answer the question how conformal theories look like on the lattice with Wilson fermions, we introduce quark masses and lattice artifacts into LSM and analyze their effects to the vacuum structure.

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Velocity renormalization in graphene from lattice Monte Carlo
Timo Laehde, Joaquin Drut
Poster Session

The Coulomb interaction between quasiparticles in graphene is expected to reshape the Dirac cones by means of a logarithmic running of the Fermi velocity. I will report a recent lattice Monte Carlo calculation of the quasiparticle dispersion relation in graphene, within the Dirac low-energy theory, augmented by an instantaneous, long-range Coulomb interaction.

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Dynamical 2+1 flavor QCD + QED
Gerrit Schierholz
Poster Session

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