Operator dynamics in Floquet many-body systems

TL;DR

This paper investigates operator dynamics in Floquet many-body quantum systems, revealing unique late-time autocorrelation tails linked to time-translation symmetry, and compares these features with random-in-time quantum circuits.

Contribution

It identifies distinctive autocorrelation tail behavior in Floquet systems and compares operator dynamics across different types of quantum circuits, highlighting the effects of time-translation symmetry.

Findings

Autocorrelation functions in Floquet systems exhibit late-time tails growing with operator size.

Spectral form factor deviations from random matrix theory are explained by autocorrelation tails.

No new behaviors are observed in OTOCs for Floquet models compared to random-in-time circuits.

Abstract

We study operator dynamics in many-body quantum systems, focusing on generic features of systems that are ergodic, spatially extended, and lack conserved densities. Quantum circuits of various types provide simple models for such systems. We focus on Floquet quantum circuits, comparing their behaviour with what has been found previously for circuits that are random in time. Floquet circuits, which have discrete time-translation symmetry, represent an intermediate case between circuits that are random in time and lack any symmetry, and systems with a time-independent Hamiltonian and continuous time-translation invariance. By making this comparison, one of our aims is to identify signatures of time-translation symmetry in Floquet operator dynamics. To characterise behaviour we examine a variety of quantities in solvable models and numerically: operator autocorrelation functions; the partial spectral form factor; the out-of-time-order correlator (OTOC); and the paths in operator space that make the dominant contributions to the ensemble-averaged autocorrelation functions. Our most striking result is that ensemble-averaged autocorrelation functions show behaviour that is distinctively different in Floquet systems compared to systems in which successive time-steps are independent. Specifically, while average autocorrelation functions decay on a microscopic timescale for circuits that are random in time, in Floquet systems they have a late-time tail with a duration that grows parametrically with the size of the operator support. The existence of these tails provides a way to understand deviations of the spectral form factor from random matrix behaviour at times shorter than the Thouless time. In contrast to this feature in autocorrelation functions, we find no new aspects to the behaviour of OTOCs for Floquet models compared to random-in-time circuits.