Quantum multifractality as a probe of phase space in the Dicke model

TL;DR

This paper investigates how multifractal analysis of coherent states in the Dicke model reveals detailed structures of classical phase space, including chaos and localization, serving as a sensitive quantum probe.

Contribution

It introduces a multifractal approach to analyze phase space features in the Dicke model, linking quantum multifractality with classical dynamics and addressing analysis challenges.

Findings

Multifractality distinguishes ergodic and localized states.

Multifractal analysis detects chaos and regularity in phase space.

The method complements classical tools for phase space investigation.

Abstract

We study the multifractal behavior of coherent states projected in the energy eigenbasis of the spin-boson Dicke Hamiltonian, a paradigmatic model describing the collective interaction between a single bosonic mode and a set of two-level systems. By examining the linear approximation and parabolic correction to the mass exponents, we find ergodic and multifractal coherent states and show that they reflect details of the structure of the classical phase space, including chaos, regularity, and features of localization. The analysis of multifractality stands as a sensitive tool to detect changes and structures in phase space, complementary to classical tools to investigate it. We also address the difficulties involved in the multifractal analyses of systems with unbounded Hilbert spaces.