Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential

Abstract

We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $|\ensuremath{\psi}(0)\ensuremath{\rangle}=|\ensuremath{\cdots}2020\ensuremath{\cdots}\ensuremath{\rangle}$ in the presence of a trapping potential. We compute the level spacing statistic, the time evolution of the number imbalance between the odd and the even sites, and the entanglement entropy in order to show that the system exhibits nonergodicity in a strongly interacting regime. The trapping potential enhances nonergodicity even when the trapping potential is weak compared to the hopping energy. We derive the effective spin-1/2 $XXZ$ Hamiltonian for the strongly interacting regimes by using a perturbation method. On the basis of the effective Hamiltonian, we show that the trapping potential is effectively strengthened by the on-site interaction, leading to the enhancement of the nonergodic behavior. We also calculate the real-time dynamics under the effective Hamiltonian and find that the entanglement entropy grows logarithmically in time.