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.
Highlights
It is worth emphasising up front that while for non-interacting systems the flow equation method may seem like an elaborate way to solve a problem which can be more efficiently treated by exact diagonalization, the real advantage of this method lies in its ability to non-perturbatively solve interacting quantum systems on system sizes far larger than accessible to numerically exact methods
We have demonstrated a new method for the diagonalization of Floquet quasienegy/evolution operators based around continuous unitary transforms, or ‘flow equations’
This method is a generalisation of the Wegner flow which has been used in a variety of contexts in the years since its development [56, 74]
Summary
Understanding the nonequilibrium dynamics of quantum many-body systems is a key challenge at the heart of modern research in condensed matter physics, motivated by a host of recent experimental developments in quantum simulation which have enabled unprecedented levels of control of strongly correlated quantum matter. One current frontier is the use of time-periodic drive, such as a laser or time-varying magnetic field, to engineer effective Hamiltonians, leading to new states of matter far from equilbrium [2,3,4] This line of thought, known as Floquet engineering, has recently lead to a number of dramatic experimental breakthroughs with cold atoms in dynamically modulated optical lattices, including the realization of non-trivial topological phases [5,6], the control of magnetic correlations in strongly interacting fermionic gases [7], and the experimental realization of strongly driven Fermi [8] and Bose Hubbard models [9,10], which play important roles in the quantum simulation of condensed matter systems. We conclude with an outlook towards the future and discuss possible applications of our method beyond those which we present here
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