Phase transition and critical behavior of d=3 chiral fermion models with left/right asymmetry

TL;DR

This paper studies the critical behavior of three-dimensional chiral fermion models with left/right asymmetry, identifying phase transitions and universality classes relevant to strongly correlated chiral fermions.

Contribution

It classifies four-fermion interactions in 3D chiral models and determines their critical exponents, introducing new universality classes for strongly correlated chiral fermions.

Findings

Second-order phase transition to chiral-symmetry broken phase

Critical exponents and anomalous dimensions calculated for N_L >= 1

Models define new universality classes for chiral fermion systems

Abstract

We investigate the critical behavior of three-dimensional relativistic fermion models with a U(N_L)_L x U(1)_R chiral symmetry reminiscent of the Higgs-Yukawa sector of the standard model of particle physics. We classify all possible four-fermion interaction terms and the corresponding discrete symmetries. For sufficiently strong correlations in a scalar parity-conserving channel, the system can undergo a second-order phase transition to a chiral-symmetry broken phase which is a 3d analog of the electroweak phase transition. We determine the critical behavior of this phase transition in terms of the critical exponent $\nu$ and the fermion and scalar anomalous dimensions for N_L >= 1. Our models define new universality classes that can serve as prototypes for studies of strongly correlated chiral fermions.