Critical Behaviour in the Single Flavor Planar Thirring Model

TL;DR

This paper presents lattice simulations of the 2+1 dimensional Thirring model with a focus on symmetry-breaking phase transitions and critical behavior, highlighting differences in critical exponents from previous fermion discretizations.

Contribution

It introduces a lattice simulation approach using domain wall fermions to study the Thirring model, revealing a quantum critical point with distinct critical exponents.

Findings

Identified a symmetry-breaking phase transition at strong coupling for N=1.

Measured critical exponents differing from staggered fermion results.

Demonstrated the effectiveness of domain wall fermions in preserving continuum symmetries.

Abstract

We report results of simulations of the $2+1d$ Thirring model with $N$ fermion flavors, defined on a lattice using domain wall fermions. This approach is devised to respect as far as possible the underlying U($2N$) symmetry of the continuum model, expected to be recovered in the limit wall separation $L_s\to\infty$. For $N=1$ there is a symmetry-breaking phase transition associated with bilinear condensation at strong fermion self-interaction, which is a plausible location for a quantum critical point. Fits to a renormalisation group-inspired equation of state yield critical exponents distinct from those obtained using a version of the model defined using staggered fermions.