Chaos and Thermalization in the Spin-Boson Dicke Model

TL;DR

This paper investigates how chaos in the spin-boson Dicke model leads to thermalization, validating the eigenstate thermalization hypothesis through entropy measures and highlighting the benefits of an efficient basis for analysis.

Contribution

It demonstrates the connection between chaos and thermalization in the Dicke model and introduces the efficient basis as a superior method for studying its spectrum.

Findings

Eigenstate expectation values support ETH in the chaotic region.

Chaotic eigenstates exhibit high von Neumann and Shannon entropy.

Efficient basis allows access to more converged states than Fock basis.

Abstract

We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called "efficient basis" over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.