Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology

TL;DR

This paper demonstrates that crossings in the entanglement spectrum during quantum quenches serve as robust signatures of non-Hermitian topological phases in open quantum many-body systems, revealing unique quantum phenomena.

Contribution

It introduces entanglement spectrum crossings as a novel dynamical signature of non-Hermitian topology in quantum many-body systems, supported by analytical and numerical analysis.

Findings

Entanglement spectrum crossings occur at topological transitions.

The first crossing time diverges with a critical exponent of 1/2.

Exact solutions interpret the dynamics as a fermion parity pump.

Abstract

The development of non-Hermitian topological band theory has led to observations of novel topological phenomena in effectively classical, driven and dissipative systems. However, for open quantum many-body systems, the absence of a ground state presents a challenge to define robust signatures of non-Hermitian topology. We show that such a signature is provided by crossings in the time evolution of the entanglement spectrum. These crossings occur in quenches from the trivial to the topological phase of a driven-dissipative Kitaev chain that is described by a Markovian quantum master equation in Lindblad form. At the topological transition, which can be crossed either by changing parameters of the Hamiltonian of the system or by increasing the strength of dissipation, the time scale at which the first entanglement spectrum crossing occurs diverges with a dynamical critical exponent of $\epsilon = 1/2$. We corroborate these numerical findings with an exact analytical solution of the quench dynamics for a spectrally flat postquench Liouvillian. This exact solution suggests an interpretation of the topological quench dynamics as a fermion parity pump. Our work thus reveals signatures of non-Hermitian topology which are unique to quantum many-body systems and cannot be emulated in classical simulators of non-Hermitian wave physics.