Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices

TL;DR

This paper investigates the spectral properties of the Liouvillian in a dissipative quantum system, revealing distinct signatures of integrability and chaos across phase transitions, and introduces a method to classify quantum dynamics in open systems.

Contribution

It establishes a link between dissipative quantum phase transitions and non-Hermitian random matrix theory using the dissipative Dicke model, highlighting spectral signatures of chaos and integrability.

Findings

Liouvillian spectra show Poisson and Ginibre distributions in different phases.

The complex-level spacing ratio distribution distinguishes phases.

Method can classify quantum dynamics in other open systems.

Abstract

We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory. For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in open quantum systems. We establish that the Liouvillian describing the quantum dynamics exhibits distinct spectral features of integrable and chaotic character on the two sides of the critical point. We follow the distribution of the spacings of the complex Liouvillian eigenvalues across the critical point. In the normal and superradiant phases, the distributions are $2D$ Poisson and that of the Ginibre Unitary random matrix ensemble, respectively. Our results are corroborated by computing a recently introduced complex-plane generalization of the consecutive level-spacing ratio distribution. Our approach can be readily adapted for classifying the nature of quantum dynamics across dissipative critical points in other open quantum systems.