# Roopayan Ghosh: A Floquet perturbation theory for periodically driven weakly-interacting fermions

We compute the Floquet Hamiltonian H_F 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 ~ω_D ≥ V_0 J_0 , where J_0 is the amplitude of the kinetic term, ω_D is the drive frequency, and V_0 is the typical interaction strength between the fermions. We compute, for random initial states, the fidelity F between wavefunctions after a drive cycle obtained using H_F and that obtained using exact diagonalization (ED). We find that FPT yields a substantially larger value of F compared to its Magnus counterpart for V_0 ≤ ~ω_D and V_0 J_0 . We use the H_F obtained to study the nature of the steady state of a weakly interacting fermion chain; we find a wide range of ω_D which leads to subthermal or superthermal steady states for finite chains. The driven fermionic chain displays perfect dynamical localization for V_0 = 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.

Journal Ref:- Phys. Rev. B 102, 235114 – Published 4 December 2020