Topological invariants of worldlines as a novel way to characterize entanglement

Yu-Long Zhang, Cheng-Ming Miao, Qing‐Feng Sun +2 more

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 second-order 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. Higher-order topological insulators have become a focus of research, but developing a universal way to characterize their unique higher-order topological properties remains a key challenge. The authors propose an entanglement topological invariant based on entanglement entropy, which not only reliably identifies second-order topological phases but also quantifies the number of topologically protected corner states.

김종현

Dmitry Melnikov

Fabio Lingua, Wei Wang, Liana Shpani +1 more

In this manuscript, we present a proposal to relate topological structure of worldline configurations to multipartite entanglement. Configurations result from the path-integral formulation of the density matrix in the limit of zero temperature. We consider hard-core bosons for which configurations, i.e. collections of particle paths, can be seen as geometric braids with a certain topological structure. We propose that properties of worldline configurations may realize a comprehensive deciphering of multipartite entanglement. By means of Monte Carlo calculations, we study checkerboard, stripe, valence-bond solids, $\mathbb{Z}_2$ topologically ordered spin liquid, and superfluid phase. We find that each ground-state is characterized by a certain `topological spectrum' which can be used to differentiate among different ground-states.

Zhong Wang, Shoucheng Zhang

Topological insulators are classified by ``topological invariants'' characterizing their electronic structures. Identifying and computing topological invariants for insulators in which electron-electron interactions are important is, however, difficult. Theorists now present a way to accomplish this task for a wide range of topological insulators.

Elisa De Ranieri