Flow Equations for Disordered Floquet Systems

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.

40 pages, 10 figures

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Cited by in corpus (13)

• Many-Body Localization in the Age of Classical Computing
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Catching thermal avalanches in the disordered XXZ model
• Efficient flow equations for dissipative systems
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• Anomalous Floquet Phases. A resonance phenomena
• Unraveling long-time quantum dynamics using flow equations
• Flow-equation approach to quantum systems driven by an amplitude-modulated time-periodic force
• Measuring out quasi-local integrals of motion from entanglement
• Disorder-induced spin-charge separation in the 1-D Hubbard model
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• The exact solution of the Wegner flow equation with the Mielke generator for $3\times 3$ Hermitian matrices
• Investigating Stark many-body localization with continuous unitary transformation flows