arXiv subjects

Christof Gattringer

Publications and source records attributed to Christof Gattringer.

At least 19 recordsLinked to original sources

arXiv2025

U(1)-gauged 2-flavor spin system in 3-D

We study a U(1)-gauged 2-component spin system in 3 dimensions. For the gauge fields we use the Villain formulation with a constraint that removes lattice monopoles and in this form couple the gauge fields to 2-component spins. We discuss the simulation strategies for this highly constraint system and present first results for the phase structure. Our preliminary Monte Carlo simulations indicate that the system undergoes a second order phase transition driven by the spin coupling. However, the correlation length critical exponent is inconsistent with the conformal bootstrap constraint for a critical (rather than multi-critical) fixed point, which forces a conclusion that the transition is likely weakly 1st order, passing close to a multi-critical point. To reliably resolve the nature of the transition, simulations on larger lattices will be necessary.

hep-lat↗

arXiv2022

Density of states techniques for fermion worldlines

Worldline representations were established as a powerful tool for studying bosonic lattice field theories at finite density. For fermions, however, the worldlines still may carry signs that originate from the Dirac algebra and from the Grassmann nature of the fermion fields. We show that a density of states approach can be set up to deal with this remaining sign problem, where finite density is implemented in a canonical approach by working with a fixed winding number of the fermion worldlines. We discuss the approach in detail and show first results of a numerical implementation in 2 dimensions.

hep-lat↗

arXiv2022

Massless Schwinger model with a 4-fermi interaction at topological angle $θ= π$

We study the massless Schwinger model with an additional 4-fermi interaction and a topological term. For topological angle $θ= π$ charge conjugation symmetry is implemented in a non-trivial way and we study the possibility of its spontaneous breaking. For the lattice discretization we use staggered fermions and the Villain action for the gauge fields, where the topological term is an integer and charge conjugation at $θ= π$ is an exact symmetry. The complex action problem is overcome by a suitable worldline/worldsheet representation. We find that as a function of the 4-fermi coupling the system shows a critical point separating a weak coupling phase where charge conjugation symmetry is intact from a strong coupling phase with spontaneously broken charge conjugation symmetry.

hep-lat↗

arXiv2022

Phase structure of self-dual lattice gauge theories in 4d

We discuss U(1) lattice gauge theory models based on a modified Villain formulation of the gauge action, which allows coupling to bosonic electric and magnetic matter. The formulation enjoys a duality which maps electric and magnetic sectors into each other. We propose several generalizations of the model and discuss their 't~Hooft anomalies. A particularly interesting class of theories is the one where electric and magnetic matter fields are coupled with identical actions, such that for a particular value of the gauge coupling the theory has a self-dual symmetry. The self-dual symmetry turns out to be a generator of a group which is a central extension of $\mathbb Z_4$ by the lattice translation symmetry group. The simplest case amenable to numerical simulations is the case when there is exactly one electrically and one magnetically charged boson. We discuss the phase structure of this theory and the nature of the self-dual symmetry in detail. Using a suitable worldline representation of the system we present the results of numerical simulations that support the conjectured phase diagram.

hep-th↗

arXiv2022

Self-dual U(1) lattice field theory with a $θ$-term

We study U(1) gauge theories with a modified Villain action. Such theories can naturally be coupled to electric and magnetic matter, and display exact electric-magnetic duality. In their simplest formulation without a $θ$-term, such theories are ultra-local. We extend the discussion to U(1) gauge theories with $θ$-terms, such that $θ$ periodicity is exact for a free theory, and show that imposing electric-magnetic duality results in a local, but not ultra-local lattice action, which is reminiscent of the Lüscher construction of axial-symmetry preserving fermions in 4d. We discuss the coupling to electric and magnetic matter as well as to dyons. For dyonic matter the electric-magnetic duality and shifts of the $θ$-angle by $2π$ together generate an SL$(2,\mathbb Z)$ duality group of transformations, just like in the continuum. We finally illustrate how the SL$(2,\mathbb Z)$ duality may be used to explore theories at finite $θ$ without a sign problem.

hep-lat↗

arXiv2021

Density of states approach for lattice field theory with topological terms

We discuss a new density of states (DoS) approach to solve the complex action problem that is caused by topological terms. The key ingredient is to use open boundary conditions for (at least) one of the directions, such that the quantization of the topological charge is lifted and the density becomes a regular function. We employ the DoS FFA method and compute the density of states as a function of the topological charge. Subsequent integration with suitable factors gives rise to the observables we are interested in. We here explore two test cases: U(1) lattice gauge theory in two dimensions, and SU(2) lattice gauge theory in four dimensions. Since the 2-d case has an exact solution we may use it to assess the method, in particular to establish the equivalence of the open boundary results with the usual choice of periodic boundary conditions. The SU(2) case is a first step of developing the techniques towards their eventual application in full QCD.

hep-lat↗

arXiv2021

Numerical simulation of self-dual U(1) lattice field theory with electric and magnetic matter

We study a recently proposed formulation of U(1) lattice field theory with electric and magnetic matter based on the Villain formulation. This discretization allows for a duality that gives rise to relations between weak and strong gauge coupling. There exists a self-dual value of the gauge coupling where one may study the model as a function of the remaining matter coupling. Using Monte Carlo simulations based on a worldline/worldsheet representation of the system we evaluate order parameters for spontaneous breaking of self-duality. We find that in some interval of the matter coupling self-duality becomes broken spontaneously. We determine the endpoints of this interval and study the nature of the corresponding critical points. Finally we explore the system away from the self-dual gauge coupling and show that when crossing the self-dual point a first order jump is seen in the order parameters.

hep-lat↗

arXiv2020

First-principle simulations of 1+1d quantum field theories at $θ=π$ and spin-chains

We present a lattice study of a 2-flavor $U(1)$ gauge-Higgs model quantum field theory with a topological term at $θ=π$. Such studies are prohibitively costly in the standard lattice formulation due to the sign-problem. Using a novel discretization of the model, along with an exact lattice dualization, we overcome the sign-problem and reliably simulate such systems. Our work provides the first ab initio demonstration that the model is in the spin-chain universality class, and demonstrates the power of the new approach to $U(1)$ gauge theories.

cond-mat.str-el↗

arXiv2020

Density of states approach for lattice gauge theory with a $θ$-term

We discuss a new strategy for treating the complex action problem of lattice field theories with a $θ$-term based on density of states (DoS) methods. The key ingredient is to use open boundary conditions where the topological charge is not quantized to integers and the density of states is sufficiently well behaved such that it can be computed precisely with recently developed DoS techniques. After a general discussion of the approach and the role of the boundary conditions, we analyze the method for 2-d U(1) lattice gauge theory with a $θ$-term, a model that can be solved in closed form. We show that in the continuum limit periodic and open boundary conditions describe the same physics and derive the DoS, demonstrating that only for open boundary conditions the density is sufficiently well behaved for a numerical evaluation. We conclude our proof of principle analysis with a small test simulation where we numerically compute the density and compare it with the analytical result.

hep-lat↗

arXiv2020

Exploring the worldline formulation of the Potts model

We revisit the issue of worldline formulations for the q-state Potts model and discuss a worldline representation in arbitrary dimensions which also allows for magnetic terms. For vanishing magnetic field we implement a Hodge decomposition for resolving the constraints with dual variables, which in two dimensions implies self-duality as a simple corollary. We present exploratory 2-d Monte Carlo simulations in terms of the worldlines, based on worm algorithms. We study both, vanishing and non-zero magnetic field, and explore q between q = 2 and q = 30, i.e., Potts models with continuous, as well as strong first order transitions.

hep-lat↗

arXiv2019

New DoS approaches to finite density lattice QCD

We present two new suggestions for density of states (DoS) approaches to finite density lattice QCD. Both proposals are based on the recently developed and successfully tested DoS FFA technique, which is a DoS approach for bosonic systems with a complex action problem. The two different implementations of DoS FFA we suggest for QCD make use of different representations of finite density lattice QCD in terms of suitable pseudo-fermion path integrals. The first proposal is based on a pseudo-fermion representation of the grand canonical QCD partition sum, while the second is a formulation for the canonical ensemble. We work out the details of the two proposals and discuss the results of exploratory 2-d test studies for free fermions at finite density, where exact reference data allow one to verify the final results and intermediate steps.

hep-lat↗

arXiv2019

New canonical and grand canonical DoS techniques for finite density lattice QCD

We discuss two new DoS approaches for finite density lattice QCD. The paper extends a recent presentation of the new techniques based on Wilson fermions, while here we now discuss and test the case of finite density QCD with staggered fermions. The first of our two approaches is based on the canonical formulation where observables at a fixed net quark number $N$ are obtained as Fourier moments of the vacuum expectation values at imaginary chemical potential $θ$. We treat the latter as densities which can be computed with the recently developed FFA method. The second approach is based on a direct grand canonical evaluation after rewriting the QCD partition sum in terms of a suitable pseudo-fermion representation. In this form the imaginary part of the pseudo-fermion action can be identified and the corresponding density may again be computed with FFA. We develop the details of the two approaches and discuss some exploratory first tests for the case of free fermions where reference results for assessing the new techniques may be obtained from Fourier transformation.

hep-lat↗

arXiv2019

Baryon bag simulation of QCD in the strong coupling limit

We explore the possibility of a simulation of strong coupling QCD in terms of so-called baryon bags. In this form the known representation in terms of monomers, dimers and baryon loops is reorganized such that the baryon contributions are collected in space time domains referred to as baryon bags. Within the bags three quarks propagate coherently as a baryon that is described by a free fermion, whereas the rest of the lattice is solely filled with interacting meson terms, i.e., quark and diquark monomers and dimers. We perform a simulation directly in the baryon bag language using a newly developed worm update and show first results in two dimensions.

hep-lat↗

arXiv2019

Topology and index theorem with a generalized Villain lattice action -- a test in 2d

Using 2-d U(1) lattice gauge theory we study two definitions of the topological charge constructed from a generalized Villain action and analyze the implementation of the index theorem based on the overlap Dirac operator. One of the two definitions expresses the topological charge as a sum of the Villain variables and treats charge conjugation symmetry exactly, making it particularly useful for studying related physics. Our numerical analysis establishes that for both topological charge definitions the index theorem becomes exact quickly towards the continuum limit.

hep-lat↗

arXiv2019

Abelian gauge theories on the lattice: $θ$-terms and compact gauge theory with(out) monopoles

We discuss a particular lattice discretization of abelian gauge theories in arbitrary dimensions. The construction is based on gauging the center symmetry of a non-compact abelian gauge theory, which results in a Villain type action. We show that this construction has several benefits over the conventional $U(1)$ lattice gauge theory construction, such as electric-magnetic duality, natural coupling of the theory to magnetically charged matter in four dimensions, complete control over the monopoles and their charges in three dimensions and a natural $θ$-term in two dimensions. Moreover we show that for bosonic matter our formulation can be mapped to a worldline/worldsheet representation where the complex action problem is solved. We illustrate our construction by explicit dualizations of the $CP(N\!-\!1)$ and the gauge Higgs model in $2d$ with a $θ$ term, as well as the gauge Higgs model in $3d$ with constrained monopole charges. These models are of importance in low dimensional anti-ferromagnets. Further we perform a natural construction of the $θ$-term in four dimensional gauge theories, and demonstrate the Witten effect which endows magnetic matter with a fractional electric charge. We extend this discussion to $PSU(N)=SU(N)/\mathbb Z_N$ non-abelian gauge theories and the construction of discrete $θ$-terms on a cubic lattice.

hep-lat↗

arXiv2018

Bag representation for composite degrees of freedom in lattice gauge theories with fermions

We explore new representations for lattice gauge theories with fermions, where the space-time lattice is divided into dynamically fluctuating regions, inside which different types of degrees of freedom are used in the path integral. The first kind of regions is a union of so-called bags, in which the dynamics is described by the free propagation of composite degrees of freedom of the original fermions. In the second region, called complementary domain, configurations of the remaining interacting degrees of freedom are used to describe the dynamics. We work out the bag representation for the gauge groups SU(2) and SU(3) and address the nature of the strong coupling effective degrees of freedom, which are fermions for SU(3) and bosons for SU(2). We discuss first steps towards a numerical simulation of the bag representations.

hep-lat↗

arXiv2018

The critical endpoint in the 2d U(1) gauge-Higgs model at topological angle $θ=π$

We study 2d U(1) gauge Higgs systems with a $θ$-term. For properly discretizing the topological charge as an integer we introduce a mixed group- and algebra-valued discretization (MGA scheme) for the gauge fields, such that the charge conjugation symmetry at $θ= π$ is implemented exactly. The complex action problem from the $θ$-term is overcome by exactly mapping the partition sum to a worldline/worldsheet representation. Using Monte Carlo simulation of the worldline/worldsheet representation we study the system at $θ= π$ and show that as a function of the mass parameter the system undergoes a phase transition. Determining the critical exponents from a finite size scaling analysis we show that the transition is in the 2d Ising universality class. We furthermore study the U(1) gauge Higgs systems at $θ= π$ also with charge 2 matter fields, where an additional $Z_2$ symmetry is expected to alter the phase structure. Our results indicate that for charge 2 a true phase transition is absent and only a rapid crossover separates the large and small mass regions.

hep-lat↗

arXiv2018

Low temperature condensation and scattering data

We study $ϕ^4$ lattice field theory at finite chemical potential $μ$ in two and four dimensions, using a worldline representation that overcomes the complex action problem. We compute the particle number at very low temperature as a function of $μ$ and determine the first three condensation thresholds, where the system condenses 1, 2 and 3 particles. The corresponding critical values of the chemical potential can be related to the 1-, 2- and 3-particle energies of the system, and we check this relation with a direct spectroscopy determination of the $n$-particle energies from $2n$-point functions. We analyze the thresholds as a function of the spatial size of the system and use the known finite volume results for the $n$-particle energies to relate the thresholds to scattering data. For four dimensions we determine the scattering length from the 2-particle threshold, while in two dimensions the full scattering phase shift can be determined. In both cases the scattering data computed from the 2-particle threshold already allow one to determine the 3-particle energy. In both, two and four dimensions we find very good agreement of this ''prediction'' with direct determinations of the 3-particle energy from either the thresholds or the 6-point functions. The results show that low temperature condensation is indeed governed by scattering data.

hep-lat↗