Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries

TL;DR

This paper shows that the entanglement spectrum dynamics in periodic open quantum systems can reveal topological phase transitions, even with the non-Hermitian skin effect, by analyzing zero-crossings after quenches.

Contribution

It demonstrates that topological phase transitions in open quantum systems can be detected through entanglement spectrum dynamics under periodic boundary conditions, despite the presence of NHSE/LSE.

Findings

Zero-crossings in entanglement spectrum indicate topological phase transitions.

Entanglement spectrum dynamics reveal topological properties in systems with skin effects.

Topological phases leave detectable signatures in subsystem dynamics.

Abstract

It has recently been established that open quantum systems may exhibit a strong spectral sensitivity to boundary conditions, known as the non-Hermitian/Liouvillian skin effect (NHSE/LSE), making the topological properties of the system boundary-condition sensitive. In this Letter, we ask the query: Can topological phase transitions of open quantum systems, captured by open boundary conditioned invariants, be observed in the dynamics of a system in a periodic boundary condition, even in the presence of NHSE/LSE? We affirmatively respond to this question, by considering the quench dynamics of entanglement spectrum in a periodic open quantum fermionic system. We demonstrate that the entanglement spectrum exhibits zero-crossings only when this periodic system is quenched from a topologically trivial to non-trivial phase, defined from the spectrum in open boundary conditions, even in systems featuring LSE. Our results reveal that non-Hermitian topological phases leave a distinctive imprint on the unconditional dynamics within a subsystem of fermionic systems.