Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble

TL;DR

This paper investigates how entanglement entropy behaves in non-Hermitian quantum systems modeled by the Ginibre ensemble, revealing suppressed entropy growth and universal features in dissipative quantum chaos.

Contribution

It introduces the entanglement spectrum for non-Hermitian eigenstates and demonstrates universality across different models like the nSYK.

Findings

Entanglement entropy is suppressed in non-Hermitian chaotic systems.

The entanglement spectrum has infinite support in the complex plane.

Universal behavior observed in Ginibre ensemble and nSYK model.

Abstract

Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show that for Hamiltonians displaying non-Hermitian many-body quantum chaos, modeled by the Ginibre ensemble, the entanglement entropy of typical eigenstates is greatly suppressed. The entropy does not grow with the Hilbert space dimension for sufficiently large systems and the fluctuations are of equal order. We derive the novel entanglement spectrum that has infinite support in the complex plane and strong energy dependence. We provide evidence of universality and similar behavior is found in the non-Hermitian Sachdev-Ye-Kitaev (nSYK) model, indicating the general applicability of the Ginibre ensemble to dissipative many-body quantum chaos.