Nontrivial worldline winding in non-Hermitian quantum systems
Shi-Xin Hu, Yongxu Fu, Yi Zhang
Abstract
Amid the growing interest in non-Hermitian quantum systems, noninteracting 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 convergence. 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 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 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.