A many-body marker for three-dimensional topological insulators with inversion symmetry

TL;DR

This paper introduces a many-body marker for three-dimensional topological insulators with inversion symmetry, enabling the detection of topological phases in interacting systems beyond mean-field methods.

Contribution

It extends a previous 2D topological marker to 3D systems, applicable to interacting insulators and compatible with quantum Monte Carlo techniques.

Findings

Successfully distinguishes trivial, weak, and strong topological insulators in 3D.

Reproduces correct non-interacting limit results.

Applicable to interacting systems beyond mean-field approximations.

Abstract

We extend the previously defined many-body marker for two-dimensional $\mathbb{Z}_2$ topological insulators [I. Gilardoni {\it et al.}, Phys. Rev. B {\bf 106}, L161106 (2022)] to distinguish trivial, weak-, and strong-topological insulators in three dimensions, in presence of the inversion symmetry. The marker is written in term of ground-state expectation values of position operators and can be employed to detect topological phases of interacting systems beyond mean-field approximations, e.g., within quantum Monte Carlo techniques. Here, we show that the correct results of the non-interacting limit are reproduced by the many-body marker.