Quantum Monte Carlo study of strange correlator in interacting topological insulators

TL;DR

This paper uses large-scale quantum Monte Carlo simulations to show that the strange correlator effectively detects symmetry-protected topological phases and phase transitions in interacting topological insulators, especially in the Kane-Mele-Hubbard model.

Contribution

It demonstrates that the strange correlator is a robust, easy-to-implement tool for identifying topological phases and transitions in interacting fermionic systems, outperforming other methods.

Findings

Strange correlator detects phase transition from quantum spin Hall to Mott insulator.

Interaction effects on edge states are captured by strange correlator measurements.

Strange correlator is more robust and easier to implement than other numerical diagnostics.

Abstract

Distinguishing the nontrivial symmetry-protected topological (SPT) phase from the trivial insulator phase in the presence of electron-electron interaction is an urgent question to the study of topological insulators, due to the fact that most of the topological indices defined for free electron systems are very likely unsuitable for interacting cases. In this work, we demonstrate that the strange correlator is a sensitive diagnosis to detect SPT states in interacting systems. Employing large-scale quantum Monte Carlo (QMC) simulations, we investigate the interaction-driven quantum phase transition in the Kane-Mele-Hubbard model. The transition from the quantum spin Hall insulator at weak interaction to an antiferromagnetic Mott insulator at strong interaction can be readily detected by the momentum space behavior of the strange correlator in single-particle, spin, and pairing sectors. The interaction effects on the symmetry-protected edge states in various sectors, i.e., the helical Luttinger liquid behavior, are well captured in the QMC measurements of strange correlators. Moreover, we demonstrate that the strange correlator is technically easier to implement in QMC and more robust in performance than other proposed numerical diagnoses for interacting topological states, as only static correlations are needed. The attempt in this work paves the way for using the strange correlator to study interaction-driven topological phase transitions in fermionic as well as bosonic systems.