Entanglement and Correlation Spreading in non-Hermitian Spin Chains

TL;DR

This paper investigates how quantum information and correlations spread in a non-Hermitian spin chain after a quench, revealing two dynamical phases with distinct entanglement and correlation growth behaviors, including faster-than-Lieb-Robinson spreading.

Contribution

The study provides an exact solution for non-Hermitian spin chains, characterizing entanglement and correlation dynamics, and identifies two distinct dynamical phases with analytical results.

Findings

Two dynamical phases with different entanglement growth behaviors

Correlation spreading faster than Lieb-Robinson bound in one phase

Logarithmic scaling of entanglement entropy with system size

Abstract

Non-Hermitian quantum many-body systems are attracting widespread interest for their exotic properties, including unconventional quantum criticality and topology. Here we study how quantum information and correlations spread under a quantum quench generated by a prototypical non-Hermitian spin chain. Using the mapping to fermions we solve exactly the problem and compute the entanglement entropy and the correlation dynamics in the thermodynamic limit. Depending on the quench parameters, we identify two dynamical phases. One is characterized by rapidly saturating entanglement and correlations. The other instead presents a logarithmic growth in time, and correlations spreading faster than the Lieb-Robinson bound, with collapses and revivals giving rise to a modulated light-cone structure. Here, in the long-time limit, we compute analytically the entanglement entropy that we show to scale logarithmically with the size of the cut, with an effective central charge that we obtain in closed form. Our results provide an example of an exactly solvable non-Hermitian many-body problem that shows rich physics including entanglement and spectral transitions.