The disordered Dicke model

TL;DR

This paper investigates the disordered Dicke model with random spin-boson couplings, revealing how disorder affects quantum and thermal phase transitions, including the disappearance of the quantum phase transition at high disorder levels.

Contribution

The study introduces the disordered Dicke model, derives analytical expressions for phase transition conditions under disorder, and explores the impact of disorder on quantum and thermal phase transitions.

Findings

Quantum phase transition critical point decreases with increasing disorder.

No quantum phase transition occurs beyond a certain disorder threshold.

Finite temperature transition persists even with zero mean coupling if disorder is high.

Abstract

We introduce and study the disordered Dicke model in which the spin-boson couplings are drawn from a random distribution with some finite width. Regarding the quantum phase transition we show that when the standard deviation $\sigma$ of the coupling strength gradually increases, the critical value of the mean coupling strength $\mu$ gradually decreases and after a certain $\sigma$ there is no quantum phase transition at all; the system always lies in the super-radiant phase. We derive an approximate expression for the quantum phase transition in the presence of disorder in terms of $\mu$ and $\sigma$, which we numerically verify. Studying the thermal phase transition in the disordered Dicke model, we obtain an analytical expression for the critical temperature in terms of the mean and standard deviation of the coupling strength. We observe that even when the mean of the coupling strength is zero, there is a finite temperature transition if the standard deviation of the coupling is sufficiently high. Disordered couplings in the Dicke model will exist in quantum dot superlattices, and we also sketch how they can be engineered and controlled with ultracold atoms or molecules in a cavity.