Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems

TL;DR

This paper proves that high-frequency periodic driving in many-body systems leads to a quasi-conserved effective Hamiltonian, resulting in prethermalization and exponentially slow energy absorption, with implications for experimental realization of topological states.

Contribution

It establishes the existence of a quasi-conserved quantity and analyzes the dynamics and heating timescales in driven many-body systems at high frequencies.

Findings

Systems have a quasi-conserved Hamiltonian $H_*$ approximating dynamics.

Energy absorption rate is exponentially small in driving frequency.

Prethermalization occurs with slow heating up to an infinite-temperature state.

Abstract

We establish some general dynamical properties of lattice many-body systems that are subject to a high-frequency periodic driving. We prove that such systems have a quasi-conserved extensive quantity $H_*$, which plays the role of an effective static Hamiltonian. The dynamics of the system (e.g., evolution of any local observable) is well-approximated by the evolution with the Hamiltonian $H_*$ up to time $\tau_*$, which is exponentially long in the driving frequency. We further show that the energy absorption rate is exponentially small in the driving frequency. In cases where $H_*$ is ergodic, the driven system prethermalizes to a thermal state described by $H_*$ at intermediate times $t\lesssim \tau_*$, eventually heating up to an infinite-temperature state at times $t\sim \tau_*$. Our results indicate that rapidly driven many-body systems generically exhibit prethermalization and very slow heating. We briefly discuss implications for experiments which realize topological states by periodic driving.