A flow equation approach to periodically driven quantum systems

ORAL

Abstract

We present a theoretical method to generate a highly accurate time-independent Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization group-like flow equations are derived to produce the effective Hamiltonian. The method has a range of validity reaching into frequency regimes that are usually inaccessible via high frequency expansions. Our approach is demonstrated for many-body Hamiltonians where it offers an improvement over the more well-known Magnus expansion. We show how the method relates to the rotating frame approximation and how it can be used to approximately transform to a rotating frame where the exact transformation isn't tractable because infinitely many couplings are generated in an exact treatment. We compare our approximate results to those found via exact diagonalization.

*We gratefully acknowledge funding from Army Research Office Grant No. W911NF-14-1-0579, NSF Grant No. DMR-1507621, and NSF Materials Research Science and Engineering Center Grant No. DMR-1720595. We acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing computing resources . GAF acknowledges support from a Simons Fellowship.

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Presenters

  • Michael Vogl

    • Physics, University of Texas at Autin

Authors

  • Michael Vogl

    • Physics, University of Texas at Autin

  • Pontus Laurell

    • Physics, Oak Ridge National Laboratory
    • Center for Nanophase Materials Sciences, Oak Ridge National Laboratory

  • Aaron Barr

    • Physics, University of Texas at Autin
    • University of Texas at Austin

  • Gregory Fiete

    • Physics, University of Texas at Autin
    • Department of Physics, Northeastern University
    • University of Texas at Austin
    • Department of Physics, The University of Texas at Austin