Reduced density matrix and order parameters of a topological insulator

TL;DR

This paper introduces order parameters for topological insulator phases using reduced density matrices, verifies them through entanglement entropy and electronic configurations, and explores their robustness under interactions.

Contribution

It proposes a novel method to derive order parameters for topological insulators via reduced density matrices and analyzes their stability with interactions.

Findings

Topological phases are characterized by new order parameters derived from reduced density matrices.

Topological non-trivial phase remains robust under repulsive interactions.

Interactions can induce topological order in trivial regions.

Abstract

It has been recently proposed that the reduced density matrix may be used to derive the order parameter of a condensed matter system. Here we propose order parameters for the phases of a topological insulator, specifically a spinless Su-Schrieffer-Heeger (SSH) model, and consider the effect of short-range interactions. All the derived order parameters and their possible corresponding quantum phases are verified by the entanglement entropy and electronic configuration analysis results. The order parameter appropriate to the topological regions is further proved by calculating the Berry phase under twisted boundary conditions. It is found that the topological non-trivial phase is robust to the introduction of repulsive inter-site interactions, and can appear in the topological trivial parameter region when appropriate interactions are added.