Spectroscopy in the 2+1$d$ Thirring Model with $N=1$ Domain Wall Fermions

TL;DR

This study uses lattice Monte Carlo simulations with domain wall fermions to analyze the 2+1D Thirring model, revealing a large anomalous dimension at the critical point and discussing artifacts inherent to Ginsparg-Wilson fermions.

Contribution

First detailed lattice Monte Carlo analysis of the 2+1D Thirring model with domain wall fermions, highlighting unique critical behavior and artifacts.

Findings

Anomalous dimension η_ψ ≈ 3 at criticality.

Observation of symmetry breaking from U(2) to U(1)×U(1).

Identification of large early-time artifacts in correlators.

Abstract

We employ the domain wall fermion (DWF) formulation of the Thirring model on a lattice in 2+1+1 dimensions and perform $N=1$ flavor Monte Carlo simulations. At a critical interaction strength the model features a spontaneous $\mathrm{U}(2)\rightarrow\mathrm{U}(1)\otimes \mathrm{U}(1)$ symmetry breaking; we analyse the induced spin-0 mesons, both Goldstone and non-Goldstone, as well as the correlator of the fermion quasiparticles, in both resulting phases. Crucially, we determine the anomalous dimension $\eta_\psi\approx 3$ at the critical point, in stark contrast with the Gross-Neveu model in 3$d$ and with results obtained with staggered fermions. Our numerical simulations are complemented by an analytical treatment of the free fermion correlator, which exhibits large early-time artifacts due to branch cuts in the propagator stemming from unbound interactions of the fermion with its heavy doublers. These artifacts are generalisable beyond the Thirring model, being an intrinsic property of DWF, or more generally Ginsparg-Wilson fermions.