Analytic approaches to periodically driven closed quantum systems: Methods and Applications

TL;DR

This paper reviews various analytic perturbative techniques for computing the Floquet Hamiltonian in periodically driven quantum many-body systems, highlighting their applications and open problems in the field.

Contribution

It provides a comprehensive pedagogical overview of multiple analytic methods for Floquet Hamiltonian computation and discusses their applications and open challenges.

Findings

Floquet-Magnus expansion effectively analyzes driven systems.

Adiabatic-impulse approximation offers insights into slow driving regimes.

Floquet perturbation theory helps understand high-frequency driving effects.

Abstract

We present a brief overview of some of the analytic perturbative techniques for the computation of the Floquet Hamiltonian for a periodically driven, or Floquet, quantum many-body system. The key technical points about each of the methods discussed are presented in a pedagogical manner. They are followed by a brief account of some chosen phenomena where these methods have provided useful insights. We provide an extensive discussion of the Floquet-Magnus expansion, the adiabatic-impulse approximation, and the Floquet perturbation theory. This is followed by a relatively short discourse on the rotating wave approximation, a Floquet-Magnus resummation technique and the Hamiltonian flow method. We also provide a discussion of some open problems which may possibly be addressed using these methods.