Entanglement dynamics of bosons in an optical lattice

Entanglement structure characterizes quantum phases of many-body systems. Recently, entanglement entropy has been measured in a system of bosons in an optical lattice. Motivated by the experiment, we study entanglement dynamics of bosons in an optical lattice based on the Bose-Hubbard model and investigate how the dynamics of entanglement entropy characterizes the superfluid (SF) and Mott insulating (MI) phases. Specifically, we study quench dynamics from the deep MI regime by numerically calculating the Renyi entropy (RE) using the time-evolving block decimation algorithm. We find that the dynamics of RE exhibits distinct features depending on whether the system is quenched into the SF or the MI phases. When the system is quenched into the SF phase, thermalization occurs and the RE converges to a constant value in time evolution. On the other hand, when the system is quenched into the MI phase, the RE oscillates with a certain period that depends on the strength of the on-site interaction. We develop the effective theory in the strong-coupling regime and obtain an analytic expression for the time-evolution of the RE, which agrees very well with the numerical results. We thus find that the signature of the SF-MI phase transition appears in the dynamics of RE.