Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit

TL;DR

This paper investigates how mixed eigenstates in the Dicke model evolve as the system approaches the semiclassical limit, revealing a power-law decay in their relative proportion and supporting the principle of uniform semiclassical condensation.

Contribution

It introduces a phase space overlap index to classify eigenstates and demonstrates a power-law decay in mixed eigenstates with increasing system size in the Dicke model.

Findings

Power-law decay of mixed eigenstates with system size

Classification of eigenstates using Husimi functions and phase space overlap index

Support for the principle of uniform semiclassical condensation in many-body systems

Abstract

How the mixed eigenstates vary with approaching the semiclassical limit in mixed-type many-body quantum systems is an interesting but still less known question. Here, we address this question in the Dicke model, a celebrated many-body model that has a well defined semiclassical limit and undergoes a transition to chaos in both quantum and classical case. Using the Husimi function, we show that the eigenstates of the Dicke model with mixed-type classical phase space can be classified into different types. To quantitatively characterize the types of eigenstates, we study the phase space overlap index, which is defined in terms of Husimi function. We look at the probability distribution of the phase space overlap index and investigate how it changes with increasing system size, that is, when approaching the semiclassical limit. We show that increasing the system size gives rise to a power-law decay in the behavior of the relative proportion of mixed eigenstates. Our findings shed more light on the properties of eigenstates in mixed-type many-body systems and suggest that the principle of uniform semiclassical condensation of Husimi functions should also be valid for many-body quantum systems.