Symmetric Mass Generation via Multicriticality in a 3D Lattice Gross-Neveu Model

TL;DR

This study explores a 3D lattice fermion model revealing a complex phase diagram with multiple phase transitions, including a multicritical point, shedding light on mechanisms of fermion mass generation.

Contribution

It demonstrates how a three-dimensional lattice model exhibits both conventional and unconventional fermion mass generation through multicriticality and phase transition analysis.

Findings

Identified three distinct phases: massless, symmetry-broken massive, and symmetric massive.

Mapped the phase diagram in the $(U_I, U_B)$ parameter space using Monte Carlo simulations.

Discovered a multicritical point organizing the phase structure at zero coupling.

Abstract

We investigate a three-dimensional lattice model of two flavors of massless staggered fermions coupled through two independent four-fermion interactions, $U_I$ and $U_B$. Using large-scale fermion-bag Monte Carlo simulations, we map out the phase diagram in the $(U_I, U_B)$ parameter space and identify three distinct phases: a massless fermion phase, a symmetry-broken massive phase, and a symmetric massive phase. When one of the interactions is absent ($U_B=0$), the system undergoes a single continuous transition directly connecting the massless and symmetric massive phases, a feature previously associated with unconventional fermion mass generation. We find that turning on a nonzero $U_B$ separates this direct transition into two successive transitions with an intermediate symmetry-broken phase. The transition from the massless to the broken phase belongs to the Gross-Neveu universality class, while the transition from the broken to the symmetric massive phase falls into the three-dimensional XY universality class. Our results indicate that the special point at vanishing coupling, where the direct transition occurs, plays the role of a multicritical point organizing the surrounding phase structure. These findings provide a unified lattice perspective on conventional and unconventional mechanisms of fermion mass generation within a single model.