Relaxation dynamics in the driven-dissipative Su-Schrieffer-Heeger model

For a chain with an open boundary described by the non-Hermitian Hamiltonian, the combination of the algebraic damping and the non-Hermitian skin effect leads to an edge burst. It is interesting to ask whether these features remain when the system is described by a master equation with periodic drives. In this paper, taking the Su-Schrieffer-Heeger model as an example, we explore the relaxation dynamics of the system with time periodically modulated intracell tunneling and single-particle dissipations. We find that for systems with periodic boundary conditions, the relaxation in the infinite-frequency driving limit can be algebraic or exponential depending on the intracell and intercell tunneling amplitudes. Finite-frequency driving can generally open the Liouvillian gap regardless of its strength and can turn the dynamics from algebraic damping to an exponential one. The Liouvillian gap increases with the increase of the driving period until a critical driving period is reached, and then it tends to a small, nonzero value for a sufficiently slow drive. For open boundary systems, we find that the dynamics of the localized excitation is still closely related to the Liouvillian gap before the excitation reaches the system boundary. The propagation speed of the localized excitation that controls the transition relaxation timescale can be slowed down by properly increasing the driving period and amplitude.