$SO(4)$ invariant Higgs-Yukawa model with reduced staggered fermions

TL;DR

This paper investigates the phase structure of an $SO(4)$ invariant lattice Higgs-Yukawa model with reduced staggered fermions and a scalar field, revealing a continuous phase transition without fermion condensate formation.

Contribution

It extends previous four-fermion models by adding a scalar kinetic term, identifying a phase with diverging correlation length but no symmetry breaking.

Findings

No fermion condensate or symmetry breaking in certain phase region

Evidence of a continuous phase transition between massless and massive phases

Presence of a diverging correlation length indicating critical behavior

Abstract

We explore the phase structure of a four dimensional $SO(4)$ invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of $SO(4)$. The model is a generalization of a four fermion system with the same symmetries that has received recent attention because of its unusual phase structure comprising massless and massive symmetric phases separated by a very narrow phase in which a small bilinear condensate breaking $SO(4)$ symmetry is present. The generalization described in this paper simply consists of the addition of a scalar kinetic term. We find a region of the enlarged phase diagram which shows no sign of a fermion condensate or symmetry breaking but in which there is nevertheless evidence of a diverging correlation length. Our results in this region are consistent with the presence of a single continuous phase transition separating the massless and massive symmetric phases observed in the earlier work.