Three-dimensional Gross-Neveu model with two flavors of staggered fermions

TL;DR

This paper introduces a lattice field theory model with two flavors of massless staggered fermions, exploring different mechanisms of fermion mass generation at strong couplings, including spontaneous symmetry breaking and an exotic non-condensate phase.

Contribution

The paper presents a new lattice model with two fermion flavors and two types of interactions, enabling the study of distinct mass generation mechanisms within a single framework.

Findings

Identification of two massive fermion phases with different mass generation mechanisms

Model is free of sign problems and suitable for fermion bag algorithm simulations

Potential to unify understanding of various fermion mass generation phenomena

Abstract

We introduce a strongly interacting lattice field theory model containing two flavors of massless staggered fermions with two kinds of interactions: (1) a lattice current-current interaction, and (2) an on-site four-fermion interaction. At weak couplings, we expect a massless fermion phase since our interactions become irrelevant at long distances. At strong couplings, based on previous studies, we argue that our lattice model contains two different massive fermion phases with different mechanisms of fermion mass generation. In one phase, fermions become massive through Spontaneous Symmetry Breaking (SSB) via the formation of a fermion bilinear condensate. In the other phase, fermion mass arises through a more exotic mechanism without the formation of any fermion bilinear condensate. Our lattice model is free of sign problems and can be studied using the fermion bag algorithm. The longer term goal here is to study both these mass generation phenomena in a single model and understand how different phases come together.