Heating suppression via two-rate random and quasiperiodic drive protocols

TL;DR

This paper investigates how two-rate driven protocols, including random and quasiperiodic drives, can significantly slow down thermalization in a non-integrable quantum spin chain, revealing new mechanisms for heating suppression.

Contribution

It introduces and analyzes two novel two-frequency drive protocols that induce dynamical freezing and slow thermalization in a driven quantum many-body system.

Findings

Identification of parameter regimes with drastically slowed thermalization.

Existence of special $dT$ values for minimal thermalization rate.

Thue-Morse quasiperiodic drive leads to slower heating than other protocols.

Abstract

We study a random and quasiperiodically driven one-dimensional non-integrable PXP spin chain in a magnetic field for two distinct drive protocols. Each of these protocols involves square pulses with two driving frequencies which are integer multiples of each other. For the first class of protocols, the duration of the pulse is changed randomly by an amplitude $dT$ while for the second class we use a random/quasiperiodic dipolar drive, where the quasiperiodicity is implemented using the Thue-Morse (TM) or Fibonacci sequences. For both protocols, we identify parameter regimes for which the thermalization of the driven chain is drastically slowed down due to proximity to a two-rate drive induced exact dynamical freezing. We also study the properties of these driven system moving slightly away from the freezing limit. For the first type of protocols, we show the existence of special value of $dT$ for which the thermalization rate remains small and provide an analytic explanation for such slow thermalization. For the second class of protocols, in contrast to random/quasiperiodic drives involving a single frequency studied earlier, we find that the TM quasiperiodic drive leads to a distinctly slower thermalization than that for drive protocols which are either periodic or follow a random or quasiperiodic Fibonacci sequence. We provide a qualitative semi-analytic understanding of these phenomena either using an exact calculation for small system sizes or carrying out a perturbative analysis in the large drive-amplitude limit. Our analysis brings out the central role of such two-frequency protocols in the reduction of heating in driven quantum systems. We discuss experiments which can test our theory.