The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition

TL;DR

This paper investigates the lattice realization of the chiral Gross-Neveu model, revealing a Landau-forbidden phase transition where continuous chiral symmetry reemerges at strong coupling due to anomalies and beyond-mean-field effects.

Contribution

It demonstrates the emergence of chiral symmetry in a lattice model at strong coupling through numerical simulations, highlighting the importance of anomalies and non-mean-field effects.

Findings

Chiral symmetry reemerges at strong coupling in the lattice model.

A Landau-forbidden second order phase transition separates distinct symmetry-breaking phases.

Anomalies play a crucial role in enabling this unconventional phase transition.

Abstract

We study the phase diagram of the $(1+1)$-dimensional Gross-Neveu model with both $g_x^2(\bar{\psi}\psi)^2$ and $g_y^2(\bar{\psi}i\gamma_5\psi)^2$ interaction terms on a spatial lattice. The continuous chiral symmetry, which is present in the continuum model when $g_x^2=g_y^2$, has a mixed 't~Hooft anomaly with the charge conservation symmetry, which guarantees the existence of a massless mode. However, the same 't~Hooft anomaly also implies that the continuous chiral symmetry is broken explicitly in our lattice model. Nevertheless, from numerical matrix product state simulations we find that, for certain parameters of the lattice model, the continuous chiral symmetry reemerges in the infrared fixed point theory, even at strong coupling. We argue that, to understand this phenomenon, it is crucial to go beyond mean-field theory (or, equivalently, beyond the leading order term in a $1/N$ expansion). Interestingly, on the lattice, the chiral Gross-Neveu model appears at a Landau-forbidden second order phase transition separating two distinct and unrelated symmetry-breaking orders. We point out the crucial role of two different 't Hooft anomalies or Lieb-Schultz-Mattis obstructions for this Landau-forbidden phase transition to occur.