Prethermal quasiconserved observables in Floquet quantum systems

TL;DR

This paper investigates prethermal quasiconserved observables in Floquet quantum systems, identifying mechanisms of their conservation and analyzing their long-term behavior through numerical and experimental methods.

Contribution

It systematically characterizes quasiconserved observables in Floquet systems, revealing two distinct mechanisms and providing methods to identify and analyze them.

Findings

Autocorrelation behavior distinguishes quasiconserved from non-conserved observables.

Energy quasiconservation occurs at high driving frequencies.

Large global rotations can sustain quasiconservation at moderate frequencies.

Abstract

Prethermalization, by introducing emergent quasiconserved observables, plays a crucial role in protecting Floquet many-body phases over exponentially long time, while the ultimate fate of such quasiconserved operators can signal thermalization to infinite temperature. To elucidate the properties of prethermal quasiconservation in many-body Floquet systems, here we systematically analyze infinite temperature correlations between observables. We numerically show that the late-time behavior of the autocorrelations unambiguously distinguishes quasiconserved observables from non-conserved ones, allowing to single out a set of linearly-independent quasiconserved observables. By investigating two Floquet spin models, we identify two different mechanism underlying the quasi-conservation law. First, we numerically verify energy quasiconservation when the driving frequency is large, so that the system dynamics is approximately described by a static prethermal Hamiltonian. More interestingly, under moderate driving frequency, another quasiconserved observable can still persist if the Floquet driving contains a large global rotation. We show theoretically how to calculate this conserved observable and provide numerical verification. Having systematically identified all quasiconserved observables, we can finally investigate their behavior in the infinite-time limit and thermodynamic limit, using autocorrelations obtained from both numerical simulation and experiments in solid state nuclear magnetic resonance systems.