Diagnosis of mixed-state topological phases in strongly correlated systems via disorder parameters

TL;DR

This paper introduces a numerically efficient method using disorder parameters and quantum Monte Carlo to diagnose topological phases in strongly correlated mixed states, successfully applied to models like Kane-Mele-Hubbard.

Contribution

The authors develop a new topological scaling indicator and an efficient quantum Monte Carlo algorithm to identify topological phases in interacting systems with mixed states.

Findings

Successfully mapped the transition in Kane-Mele-Hubbard model.

Identified quantum anomalous Hall phase in Haldane-Hubbard model.

Circumvented sign problem limitations in simulations.

Abstract

Characterizing topological phases for strongly interacting fermions in the mixed-state regime remains a major challenge. Here we introduce a general and numerically efficient framework to diagnose mixed-state topological phases in strongly interacting systems via the disorder parameter (DP) of the U(1) charge operator. Specifically, from the finite-size scaling of the second derivative of the DP generating function, we introduce the topological scaling indicator, which exhibits a characteristic linear scaling with the system's linear dimension for topological phases, a signature that vanishes upon transition into a topologically trivial phase. Crucially, we develop an efficient determinant Quantum Monte Carlo algorithm that facilitates the evaluation of this indicator in interacting systems. We apply our approach to two paradigmatic models: for the Kane-Mele-Hubbard model, we successfully map the interaction-driven transition from a quantum spin Hall insulator to a trivial Mott insulator. Furthermore, our method circumvents the limitations imposed by the severe sign problem in the Haldane-Hubbard model, enabling robust identification of the quantum anomalous Hall phase at accessible temperatures. This work provides a powerful and accessible tool for the numerical exploration of topological phenomena in interacting mixed states, opening a pathway to study systems previously inaccessible due to computational obstacles.