Evolution of entanglement entropy in strongly correlated bosons in an optical lattice

We study the time evolution of entanglement entropy of bosons in a one-dimensional optical lattice induced by a sudden quench of the hopping amplitude $J$. We consider the system being quenched into the deep Mott-insulating (MI) regime, i.e., $J/U\ll 1$ ($U$ is the strength of the on-site repulsive interaction), from the product state with individual boson isolated in each lattice site. The low-energy excited states in this regime can be effectively described by fermionic quasiparticles known as doublons and holons. Developing the effective theory, we analytically calculate the time evolution of the second-order R\'enyi entropy (RE) for a subsystem and propose a quasiparticle picture for the time evolution of the RE based on the obtained analytic expressions. Doublons and holons are excited by the quench as entangled pairs that propagate with the velocity $v_{\rm pair}=6J$. The RE reflects the population of doublon-holon pairs that span the boundary of the subsystem. In the short-time scale ($Jt/\hbar=\mathcal{O}(1)$), the RE exhibits the rapid oscillations with the frequency $U/\hbar$, while in the long-time scale ($Jt/\hbar\gg 1$) the RE grows linearly in time until the pair spreads beyond the size of the subsystem and the RE saturates to a constant. We analytically show that the constant value of the RE after the saturation obeys the volume-law scaling.