Dynamical freezing in the thermodynamic limit: the strongly driven ensemble

TL;DR

This paper demonstrates that strong periodic driving in a spin chain can lead to emergent conservation laws that prevent thermalization, resulting in dynamical freezing and stable entanglement properties in the thermodynamic limit.

Contribution

It introduces the concept of emergent approximate conservation laws in strongly driven systems, providing a new framework to control many-body chaos and prevent thermalization.

Findings

Emergent conservation laws prevent heating to infinite temperature.

Entanglement entropy density remains zero over long times in the thermodynamic limit.

A recipe for designing high-accuracy conservation laws is provided.

Abstract

The ergodicity postulate, a foundational pillar of Gibbsian statistical mechanics predicts that a periodically driven (Floquet) system in the absence of any conservation law heats to a featureless `infinite temperature' state. Here, we find--for a clean and interacting generic spin chain subject to a {\it strong} driving field--that this can be prevented by the emergence of {\it approximate but stable} conservation-laws not present in the undriven system. We identify their origin: they do not necessarily owe their stability to familiar protections by symmetry, topology, disorder, or even high energy costs. We show numerically, {\it in the thermodynamic limit,} that when required by these emergent conservation-laws, the entanglement-entropy density of an infinite subsystem remains zero over our entire simulation time of several decades in natural units. We further provide a recipe for designing such conservation laws with high accuracy. Finally, we present an ensemble description, which we call the strongly driven ensemble incorporating these constraints. This provides a way to control many-body chaos through stable Floquet-engineering. Strong signatures of these conservation-laws should be experimentally accessible since they manifest in all length and time scales. Variants of the spin model we have used, have already been realized using Rydberg-dressed atoms.