Exponentially slow heating in periodically driven many-body systems

TL;DR

This paper establishes that in periodically driven many-body systems with local interactions, energy absorption rates decrease exponentially with increasing driving frequency, implying long-lived topological states and metastability.

Contribution

The authors derive general bounds showing exponential decay of energy absorption rates in driven many-body systems, highlighting implications for topological states and metastability.

Findings

Energy absorption rate decays exponentially with frequency

Topological states can have very long lifetimes

Applications to cold atomic and solid-state systems

Abstract

We derive general bounds on the linear response energy absorption rates of periodically driven many-body systems of spins or fermions on a lattice. We show that for systems with local interactions, energy absorption rate decays exponentially as a function of driving frequency in any number of spatial dimensions. These results imply that topological many-body states in periodically driven systems, although generally metastable, can have very long lifetimes. We discuss applications to other problems, including decay of highly energetic excitations in cold atomic and solid-state systems.