High-frequency approximation for periodically driven quantum systems from a Floquet-space perspective

TL;DR

This paper develops a systematic high-frequency expansion method for periodically driven quantum systems, providing a unified framework that clarifies phase dependence issues and is applicable to many-body models like the Hubbard model.

Contribution

It introduces a Floquet-space based high-frequency expansion for effective Hamiltonians, unifying previous approaches and analyzing phase dependence and limitations for many-particle systems.

Findings

Derived a systematic high-frequency expansion for driven quantum systems.

Clarified the role of phase dependence and symmetry breaking.

Applied the method to a driven Hubbard model.

Abstract

We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the extended Floquet Hilbert space by means of degenerate perturbation theory. The final results are equivalent to those obtained within a different approach [Phys.\ Rev.\ A {\bf 68}, 013820 (2003), Phys.\ Rev.\ X {\bf 4}, 031027 (2014)] and can also be related to the Floquet-Magnus expansion [J.\ Phys.\ A {\bf 34}, 3379 (2000)]. We discuss that the dependence on the driving phase, which plagues the latter, can lead to artifactual symmetry breaking. The high-frequency approach is illustrated using the example of a periodically driven Hubbard model. Moreover, we discuss the nature of the approximation and its limitations for systems of many interacting particles.