Large-$S$ and tensor-network methods for strongly-interacting topological insulators

TL;DR

This paper combines large-S and tensor-network methods to investigate strongly-interacting topological insulators, revealing how varying lattice parameters induces novel phase transitions and symmetry-breaking phenomena.

Contribution

It introduces a multidisciplinary approach to study strongly-interacting topological insulators using large-S and tensor-network techniques, uncovering new phase behaviors related to lattice discretization.

Findings

Identification of spontaneous symmetry-breaking phases at strong interactions

Discovery of a novel Heisenberg-Ising compass model with critical lines

Demonstration of the impact of Wilson parameter variation on phase flow

Abstract

The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain lattice Hubbard models of topological insulators, which map onto four-Fermi quantum field theories with a Wilson-type discretization, and have been recently shown to be at reach of cold-atom quantum simulators based on synthetic spin-orbit coupling. We combine large-S and tensor-network techniques to explore the possible spontaneous symmetry-breaking phases that appear when the interactions of the topological insulators are sufficiently large. In particular, we show that varying the Wilson parameter $r$ of the lattice discretizations leads to a novel Heisenberg-Ising compass model with critical lines that flow with the value of $r$.