Out-of-equilibrium phase transitions induced by Floquet resonances in a periodically quench-driven XY spin chain

TL;DR

This paper investigates how periodic quenches in an XY spin chain induce out-of-equilibrium phase transitions, characterized by Floquet resonances, affecting the system's dynamical behavior and synchronization properties.

Contribution

It provides an exact Floquet Hamiltonian for arbitrary driving frequencies and analytically characterizes phase boundaries between local and non-local regimes.

Findings

Identification of Floquet resonances as phase transition boundaries

Analytical expressions for avoided crossings in Floquet spectrum

Distinct transient behaviors in local vs. non-local regimes

Abstract

We consider the dynamics of an XY spin chain subjected to an external transverse field which is periodically quenched between two values. By deriving an exact expression of the Floquet Hamiltonian for this out-of-equilibrium protocol with arbitrary driving frequencies, we show how, after an unfolding of the Floquet spectrum, the parameter space of the system is characterized by alternations between local and non-local regions, corresponding respectively to the absence and presence of Floquet resonances. The boundary lines between regions are obtained analytically from avoided crossings in the Floquet quasi-energies and are observable as phase transitions in the synchronized state. The transient behaviour of dynamical averages of local observables similarly undergoes a transition, showing either a rapid convergence towards the synchronized state in the local regime, or a rather slow one exhibiting persistent oscillations in the non-local regime, where explicit decay coefficients are presented.