Prethermalization without temperature

TL;DR

This paper demonstrates that in periodically driven systems, an emergent approximately conserved quantity can create a long-lived prethermal regime, enabling non-trivial dynamics and time-crystalline behavior even at high or infinite initial temperatures.

Contribution

It introduces the concept of prethermalization driven by emergent conservation laws in Floquet systems and applies it to real experimental setups, extending understanding of non-equilibrium phases.

Findings

Prethermal regimes can last significantly longer due to emergent conserved quantities.

A diagnostic method distinguishes prethermalization from many-body localization.

Modifying driving protocols can greatly extend the lifetime of Floquet time crystals.

Abstract

While a clean driven system generically absorbs energy until it reaches `infinite temperature', it may do so very slowly exhibiting what is known as a prethermal regime. Here, we show that the emergence of an additional approximately conserved quantity in a periodically driven (Floquet) system can give rise to an analogous long-lived regime. This can allow for non-trivial dynamics, even from initial states that are at a high or infinite temperature with respect to an effective Hamiltonian governing the prethermal dynamics. We present concrete settings with such a prethermal regime, one with a period-doubled (time-crystalline) response. We also present a direct diagnostic to distinguish this prethermal phenomenon from its infinitely long-lived many-body localised cousin. We apply these insights to a model of the recent NMR experiments by Rovny et al., [Phys. Rev. Lett. 120, 180603 (2018)] which, intriguingly, detected signatures of a Floquet time crystal in a clean three-dimensional material. We show that a mild but subtle variation of their driving protocol can increase the lifetime of the time-crystalline signal by orders of magnitude.