Flow Equations for Disordered Floquet Systems

TL;DR

This paper introduces a flow equation approach to analyze disordered Floquet systems, enabling direct computation of Floquet modes and local integrals of motion, and extends to many-body localized phases.

Contribution

It presents a novel flow equation method for disordered Floquet systems, including driven many-body localized phases, with improved scalability over existing techniques.

Findings

Exact solution for driven Anderson insulator

Extension to many-body localized systems

Access to larger system sizes than previous methods

Abstract

In this work, we present a new approach to disordered, periodically driven (Floquet) quantum many-body systems based on flow equations. Specifically, we introduce a continuous unitary flow of Floquet operators in an extended Hilbert space, whose fixed point is both diagonal and time-independent, allowing us to directly obtain the Floquet modes. We first apply this method to a periodically driven Anderson insulator, for which it is exact, and then extend it to driven many-body localized systems within a truncated flow equation ansatz. In particular we compute the emergent Floquet local integrals of motion that characterise a periodically driven many-body localized phase. We demonstrate that the method remains well-controlled in the weakly-interacting regime, and allows us to access larger system sizes than accessible by numerically exact methods, paving the way for studies of two-dimensional driven many-body systems.