Topological chiral currents in the Gross-Neveu model extension

TL;DR

This paper explores the connection between Lorentz-violating quantum field theories and topological phases in Hubbard models, analyzing a specific ladder model with chiral currents and mapping its phase diagram using various computational methods.

Contribution

It introduces a regularisation of the Gross-Neveu extension via a Creutz-Hubbard ladder and analyzes its topological and magnetic phases with comprehensive numerical and analytical tools.

Findings

Identification of circulating chiral currents due to Lorentz violation

Complete phase diagram including trivial, magnetic, and topological phases

Validation of theoretical predictions with numerical simulations

Abstract

We unveil an interesting connection of Lorentz-violating quantum field theories, studied in the context of the standard model extension, and Hubbard-type models of topological crystalline phases. These models can be interpreted as a regularisation of the former and, as hereby discussed, explored with current quantum simulators based on ultra-cold atoms in optical Raman lattices. In particular, we present a complete analysis of the Creutz-Hubbard ladder under a generic magnetic flux, which regularises a Gross-Neveu model extension, and presents a characteristic circulating chiral current whose non-zero value arises from a specific violation of Lorentz invariance. We present a complete phase diagram with trivial insulators, ferromagnetic and anti-ferromagnetic phases, and current-carrying topological crystalline phases. These predictions are benchmarked using tools from condensed matter and quantum-information science, showing that self-consistent Hartree-Fock and strong-coupling Dzyaloshinskii-Moriya methods capture the essence of the phase diagram in different regimes, which is further explored using extensive numerical simulations based on matrix-product states.