Z2 topological invariants in two dimensions from quantum Monte Carlo

TL;DR

This paper demonstrates how quantum Monte Carlo methods can be used to compute the $Z_2$ topological invariant in a two-dimensional interacting electron system, enabling the study of topological phase transitions.

Contribution

It introduces a practical approach to calculate the $Z_2$ invariant from QMC data in interacting systems with spin-orbit coupling.

Findings

Successfully computed the $Z_2$ invariant in an interacting model.

Analyzed the transition from trivial to topological insulator phases.

Discussed the feasibility of topological invariant calculations within QMC.

Abstract

We employ quantum Monte Carlo techniques to calculate the $Z_2$ topological invariant in a two-dimensional model of interacting electrons that exhibits a quantum spin Hall topological insulator phase. In particular, we consider the parity invariant for inversion-symmetric systems, which can be obtained from the bulk's imaginary-time Green's function after an appropriate continuation to zero frequency. This topological invariant is used here in order to study the trivial-band to topological-insulator transitions in an interacting system with spin-orbit coupling and an explicit bond dimerization. We discuss the accessibility and behavior of this topological invariant within quantum Monte Carlo simulations.