Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems

TL;DR

This paper establishes rigorous bounds on the heating rate in quantum many-body systems driven by Thue-Morse quasi-periodic and random multipolar protocols, revealing slow heating timescales and describing the transient prethermal state.

Contribution

It introduces non-perturbative bounds on heating rates for aperiodically driven systems and derives an effective Hamiltonian for the prethermal state, extending understanding beyond Floquet systems.

Findings

Heating time scales as $(rac{ ext{frequency}}{g})^{-C\, ext{ln}(rac{ ext{frequency}}{g})}$

Derived a static effective Hamiltonian for the prethermal state

Numerical simulations confirm the theoretical bounds

Abstract

The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but a- and quasi-periodic driving is still limited. Here, we derive rigorous, non-perturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasi-periodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasi-periodic driving suggests that the heating time scales like $(\omega/g)^{-C\ln(\omega/g)}$ with a positive constant $C$ and a typical energy scale $g$ of the Hamiltonian, in agreement with our numerical simulations.