Dicke transition in open many-body systems determined by fluctuation effects

TL;DR

This paper investigates the Dicke transition in open many-body quantum systems, emphasizing the role of fluctuations beyond mean-field theory to understand the nature of the phase transition and the properties of self-organized states.

Contribution

It introduces a new approach combining mean-field theory with fluctuation analysis, providing a more accurate description of dissipative quantum phase transitions.

Findings

Fluctuations are essential for understanding the mixed state character of the transition.

The approach accurately predicts universal properties of self-organized phases.

Results are validated against matrix-product-state simulations.

Abstract

In recent years, one important experimental achievement was the strong coupling of quantum matter and quantum light. Realizations reach from ultracold atomic gases in high-finesse optical resonators to electronic systems coupled to THz cavities. The dissipative nature of the quantum light field and the global coupling to the quantum matter leads to many exciting phenomena such as the occurrence of dissipative quantum phase transition to self-organized exotic phases. The theoretical treatment of these dissipative hybrid systems of matter coupled to a cavity field is very challenging. Previously, often mean-field approaches were applied which characterize the emergence of self-organized phases as a zero-temperature transition for the particles, a ground-state Dicke transition. Here we develop a new approach which combines a mean-field approach with a perturbative treatment of fluctuations beyond mean-field, which becomes exact in the thermodynamic limit. We argue that these fluctuations are crucial in order to determine the mixed state (finite temperature) character of the transition and to unravel universal properties of the self-organized states. We validate our results by comparing to time-dependent matrix-product-state calculations.