Thermalization in a periodically driven fully-connected quantum Ising ferromagnet

TL;DR

This paper investigates how a fully-connected quantum Ising ferromagnet thermalizes under periodic driving, linking quantum ergodicity and classical Hamiltonian dynamics, with implications for experimental systems like coupled BECs.

Contribution

It establishes a connection between classical ergodicity and quantum thermalization in a driven fully-connected quantum Ising model, highlighting the role of Floquet spectrum statistics.

Findings

Ergodic classical dynamics leads to Wigner-Dyson Floquet spectrum and thermalization.

Regular classical dynamics prevents thermalization.

Thermalization is associated with delocalized Floquet states and eigenstate thermalization hypothesis (ETH).

Abstract

By means of a Floquet analysis, we study the quantum dynamics of a fully connected Lipkin-Ising ferromagnet in a periodically driven transverse field showing that thermalization in the steady state is intimately connected to properties of the $N\to \infty$ classical Hamiltonian dynamics. When the dynamics is ergodic, the Floquet spectrum obeys a Wigner-Dyson statistics and the system satisfies the eigenstate thermalization hypothesis (ETH): Independently of the initial state, local observables relax to the $T=\infty$ thermal value, and Floquet states are delocalized in the Hilbert space. On the contrary, if the classical dynamics is regular no thermalization occurs. We further discuss the relationship between ergodicity and dynamical phase transitions, and the relevance of our results to other fully-connected periodically driven models (like the Bose-Hubbard), and possibilities of experimental realization in the case of two coupled BEC.