Random multipolar driving: tunably slow heating through spectral engineering

TL;DR

This paper investigates how random multipolar driving in quantum many-body systems can create a tunably long prethermal regime, with heating suppressed by spectral engineering, enabling the realization of non-equilibrium phases like discrete time crystals.

Contribution

It introduces a spectral engineering approach using random multipolar sequences to control heating and extend prethermal regimes in driven quantum systems, including the analysis of Thue-Morse sequences.

Findings

Prethermal lifetime scales algebraically with driving rate as (2n+1).

Thue-Morse sequence yields exponentially long prethermal regimes.

Non-equilibrium phases like discrete time crystals can exist in these regimes.

Abstract

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the time-scale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with $n-$multipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For $n\geq1$, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent ${2n+1}$. A simple theory based on Fermi's golden rule accounts for this behaviour. The quasiperiodic Thue-Morse sequence corresponds to the $n\to \infty$ limit, and accordingly exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile non-equilibrium phases, which we illustrate with a random multipolar discrete time crystal.