Characterizing second-order topological insulators via entanglement topological invariant in two-dimensional systems

TL;DR

This paper introduces an entanglement-based topological invariant that effectively identifies and quantifies second-order topological insulators by focusing on corner state entanglement, providing a universal characterization method.

Contribution

It proposes a novel entanglement topological invariant that accurately detects second-order topological phases and correlates with corner state counts in two-dimensional systems.

Findings

Invariant is nonzero only in second-order topological phases

Invariant magnitude matches the number of protected corner states

Provides a universal criterion for higher-order topology

Abstract

Higher-order topological insulators have attracted significant interest in recent years. However, identifying a universal topological invariant capable of characterizing higher-order topology remains challenging. Here, we propose a entanglement topological invariant designed to characterize secondorder topological systems. This entanglement topological invariant captures the entanglement of topological corner states under open boundary conditions by employing a bipartite entanglement entropy method. In several representative models, the entanglement topological invariant assumes a nonzero value exclusively in the presence of second-order topology, with its magnitude exactly matching the number of topologically protected corner states. Consequently, the proposed entanglement topological invariant not only provides a clear criterion for detecting higher-order topology, but also offers a quantitative measure for the related corner states. Our study establishes a universal and precise method for characterizing higher-order topological phases, opening avenues for their fundamental understanding and future investigations.