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

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 symmetrybreaking 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 two-dimensional 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.

Automated summary

In this study, the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory are explored, with a focus on the dissipative Dicke model. The spectral features of the Liouvillian describing the quantum dynamics are investigated across the critical point, showing distinct characteristics. This approach can be applied to classify the nature of quantum dynamics across dissipative critical points in other open quantum systems.