Onset of Floquet Thermalisation

TL;DR

This paper investigates the onset of heating and non-ergodic behavior in an interacting Floquet system, revealing a threshold-driven transition to non-thermal states that are robust across various parameters and initial conditions.

Contribution

It demonstrates that Floquet heating only occurs above a certain drive amplitude threshold, with non-ergodic states exhibiting emergent conserved quantities and partial freezing.

Findings

Heating onset only below a drive amplitude threshold

Existence of non-ergodic states with finite entropy

Partial freezing of magnetization in initial states

Abstract

In presence of interactions, a closed, homogeneous (disorder-free) many-body system is believed to generically heat up to an `infinite temperature' ensemble when subjected to a periodic drive: in the spirit of the ergodicity hypothesis underpinning statistical mechanics, this happens as no energy or other conservation law prevents this. Here we present an interacting Ising chain driven by a field of time-dependent strength, where such heating onsets only below a threshold value of the drive amplitude, above which the system exhibits non-ergodic behaviour. The onset appears at {\it strong, but not fast} driving. This in particular puts it beyond the scope of high-frequency expansions. The onset location shifts, but it is robustly present, across wide variations of the model Hamiltonian such as driving frequency and protocol, as well as the initial state. The portion of nonergodic states in the Floquet spectrum, while thermodynamically subdominant, has a finite entropy. We find that the magnetisation as an {\it emergent} conserved quantity underpinning the freezing; indeed the freezing effect is readily observed, as initially magnetised states remain partially frozen {\it up to infinite time}. This result, which bears a family resemblance to the Kolmogorov-Arnold-Moser theorem for classical dynamical systems, could be a valuable ingredient for extending Floquet engineering to the interacting realm.