Periodically driven integrable systems with long-range pair potentials. (12th July 2018) - Nandy, Sourav; Sengupta, K; Sen, Arnab
Abstract: We study periodically driven closed systems with a long-ranged Hamiltonian by considering a generalized Kitaev chain with pairing terms which decay with distance as a power law characterized by exponent α . Starting from an initial unentangled state, we show that all local quantities synchronize with the driving frequency ω at late times and relax to well-defined steady state values in the thermodynamic limit and after drive cycles for any α and ω . We introduce a distance measure, , that characterizes the approach of the reduced density matrix of a subsystem of l sites to that of the final steady state. We chart out the n dependence of and identify a critical value (which depends only on the time-averaged Hamiltonian) below which they generically decay to zero as . For, in contrast, for with at least one intermediate dynamical transition. An identical behavior is found for relaxation of all non-trivial correlation functions to their steady-state values. We also study the mutual information propagation to understand the nature of the entanglement spreading in space with increasing n for such periodically driven long-ranged systems. We point out existence of qualitatively new features (absent for ) in the space-time dependence of mutual information for, where is the largest critical frequency for the dynamical transition for a given α such as the presence of multiple light cone-like structures which persists even when α is large. We also show that the space-time dependence of the mutual information of long-ranged Hamiltonians with differs qualitatively from those with for any drive frequency and relate this to the behavior of the Floquet group velocity of such driven system.