Nontrivial worldline winding in non-Hermitian quantum systems

TL;DR

This paper explores nontrivial worldline winding phenomena in interacting non-Hermitian quantum systems, revealing new topological features and their implications for entanglement entropy through quantum Monte Carlo simulations.

Contribution

It introduces the observation of nontrivial worldline winding in interacting non-Hermitian quantum systems under periodic boundary conditions, extending topological analysis beyond non-interacting models.

Findings

Nontrivial worldline winding observed under periodic boundary conditions.

Enhanced ergodicity needed for convergence in winding sectors.

Potential impact on entanglement entropy and quantum topological phenomena.

Abstract

Amid the growing interest in non-Hermitian quantum systems, non-interacting models have received the most attention. Here, through the stochastic series expansion quantum Monte Carlo method, we investigate non-Hermitian physics in interacting quantum systems, e.g., various non-Hermitian quantum spin chains. While calculations yield consistent numerical results under open boundary conditions, non-Hermitian quantum systems under periodic boundary conditions observe an unusual concentration of imaginary-time worldlines over nontrivial winding and require enhanced ergodicity between winding-number sectors for proper convergences. Such nontrivial worldline winding is an emergent physical phenomenon that also exists in other non-Hermitian models and analytical approaches. Alongside the non-Hermitian skin effect and the point-gap spectroscopy, it largely extends the identification and analysis of non-Hermitian topological phenomena to quantum systems with interactions, finite temperatures, biorthogonal basis, and periodic boundary conditions in a novel and controlled fashion. Finally, we study the direct physical implications of such nontrivial worldline winding, which bring additional, potentially quasi-long-range contributions to the entanglement entropy.