Gross-Neveu-Wilson model and correlated symmetry-protected topological phases

TL;DR

This paper explores a lattice discretization of the Gross-Neveu model to study correlated symmetry-protected topological phases, combining high-energy physics techniques with condensed matter tools, and proposes a cold-atom quantum simulation scheme.

Contribution

It introduces a Wilson-type discretization of the Gross-Neveu model as a new platform to investigate topological phases and provides a comprehensive phase diagram analysis with experimental simulation proposals.

Findings

Large-N analysis reveals a rich phase diagram with trivial, topological, and symmetry-broken phases.

The large-N approach accurately predicts phase boundaries even at N=1.

A cold-atom scheme is proposed for quantum simulation of the model.

Abstract

We show that a Wilson-type discretization of the Gross-Neveu model, a fermionic N-flavor quantum field theory displaying asymptotic freedom and chiral symmetry breaking, can serve as a playground to explore correlated symmetry-protected phases of matter using techniques borrowed from high-energy physics. A large- N study, both in the Hamiltonian and Euclidean formalisms, yields a phase diagram with trivial, topological, and symmetry-broken phases separated by critical lines that meet at a tri-critical point. We benchmark these predictions using tools from condensed matter and quantum information science, which show that the large-N method captures the essence of the phase diagram even at N = 1. Moreover, we describe a cold-atom scheme for the quantum simulation of this lattice model, which would allow to explore the single-flavor phase diagram.