Nonadiabatic dynamics of a parametrically modulated spin chain in a topologically nontrivial regime

We study the dynamics of a resonantly modulated spin chain in a strong magnetic field. The modulation of the spin-spin coupling close to twice the Larmor frequency leads to parametric resonance. The spin dynamics in the rotating frame maps on the Kitaev chain. By varying the modulation frequency, the chain can be bought into a topologically nontrivial regime. We show that in this regime, even for a closed chain, the response to slow turning on the drive becomes nonadiabatic, leading to excitations of pairs of Jordan-Wigner fermions. The system displays a history-dependent behavior. It depends on the order in which the drive parameters are changed so that they cross the boundary of the topologically nontrivial regime or start from inside this regime, given that initially the spin system is in its ground state. We also analyze the dissipative dynamics of two coupled modulated spins and the stationary distribution over the Floquet states. For decay processes associated with the energy transfer to the thermal reservoir close to the Larmor frequency (in energy units), the states can be equally populated even where the temperature of the thermal reservoir is zero.