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arXiv · 2512.09962

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

Yu-Long Zhang·Cheng-Ming Miao·Qing-Feng Sun·Jian-Jun Liu·Ying-Tao Zhang
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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.

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Yu-Long Zhang, Cheng-Ming Miao, Qing-Feng Sun, Jian-Jun Liu, Ying-Tao Zhang. 2025-12-10. Characterizing second-order topological insulators via entanglement topological invariant in two-dimensional systems. https://arxiv.org/abs/2512.09962

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