Floquet perturbation theory for periodically driven weakly interacting fermions

Roopayan Ghosh, Bhaskar Mukherjee, and K. Sengupta
Phys. Rev. B 102, 235114 – Published 4 December 2020

Abstract

We compute the Floquet Hamiltonian HF for weakly interacting fermions subjected to a continuous periodic drive using a Floquet perturbation theory (FPT) with the interaction amplitude being the perturbation parameter. This allows us to address the dynamics of the system at intermediate drive frequencies ωDV0J0, where J0 is the amplitude of the kinetic term, ωD is the drive frequency, and V0 is the typical interaction strength between the fermions. We compute, for random initial states, the fidelity F between wave functions after a drive cycle obtained using HF and that obtained using exact diagonalization (ED). We find that FPT yields a substantially larger value of F compared to its Magnus counterpart for V0ωD and V0J0. We use the HF obtained to study the nature of the steady state of an weakly interacting fermion chain; we find a wide range of ωD which leads to subthermal or superthermal steady states for finite chains. The driven fermionic chain displays perfect dynamical localization for V0=0; we address the fate of this dynamical localization in the steady state of a finite interacting chain and show that there is a crossover between localized and delocalized steady states. We discuss the implication of our results for thermodynamically large chains and chart out experiments which can test our theory.

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  • Received 23 July 2020
  • Revised 6 October 2020
  • Accepted 20 November 2020

DOI:https://doi.org/10.1103/PhysRevB.102.235114

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Roopayan Ghosh, Bhaskar Mukherjee, and K. Sengupta

  • School of Physical Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India

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Issue

Vol. 102, Iss. 23 — 15 December 2020

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