Phase diagram of a lattice fermion model with symmetric mass generation

TL;DR

This paper explores the phase diagram of a lattice fermion model with two four-fermion couplings, revealing how small interactions alter the nature of phase transitions and introduce an intermediate symmetry-breaking phase.

Contribution

It demonstrates how a nonzero four-fermion coupling splits a single quantum phase transition into two distinct transitions with an intermediate phase, providing a detailed phase diagram analysis.

Findings

Identification of a split in the phase transition structure

Verification of critical exponents consistent with existing literature

Characterization of an intermediate symmetry-breaking phase

Abstract

We study the phase structure of a model containing two flavors of massless staggered fermions interacting through two independent four-fermion couplings, UI and UB, formulated on a three-dimensional Euclidean space-time lattice. At UB = 0, this model is known to exhibit a direct second-order quantum phase transition between a massless fermion (MF) phase and a phase in which fermions acquire masses through the mechanism commonly referred to as symmetric mass generation (SMG). We demonstrate that introducing a small nonzero value of UB qualitatively alters this structure: the single exotic transition at UB = 0 splits into two distinct, conventional transitions, separated by an intermediate phase in which fermion masses arise through the standard mechanism of spontaneous symmetry breaking (SSB). The first of these is a Gross-Neveu transition separating the MF phase from the SSB-induced massive phase, while the second is a three-dimensional XY transition between the SSB phase and the SMG phase. Using the fermion-bag Monte Carlo method, we verify that the critical exponents associated with both transitions are consistent with the literature, thereby yielding a quantitative characterization of the resulting phase structure of the model.