Numerical study of the $2+1d$ Thirring model with U($2N$)-invariant fermions

TL;DR

This paper investigates the 2+1 dimensional Thirring model with U(2N)-invariant fermions using domain wall formulation, revealing differences from previous staggered fermion studies in symmetry breaking and potential mass generation.

Contribution

It adapts the domain wall approach to restore U(2N) symmetry in interacting fermion models and provides new simulation results on dynamical mass generation.

Findings

Different symmetry breaking patterns from previous studies

Evidence of potential dynamical mass generation for N< N_c

Successful adaptation of domain wall formulation for U(2N) invariance

Abstract

In 2+1 dimensions the global U($2N$) symmetry associated with massless Dirac fermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I will show how to adapt the domain wall formulation to recover the U($2N$)-invariant limit in interacting fermion models as the domain wall separation is increased. In particular, I will focus on the issue of potential dynamical mass generation in the Thirring model, postulated to take place for $N$ less than some critical $N_c$. I will present results of simulations of the model using both HMC ($N=2$) and RHMC ($N=1$) algorithms, and show that the outcome is very different from previous numerical studies of the model made with staggered fermions, where the corresponding pattern of symmetry breaking is distinct.