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

TL;DR

This paper studies how a trapping potential influences nonergodic behavior in the one-dimensional Bose-Hubbard model, revealing that even weak traps can enhance nonergodicity and lead to logarithmic entanglement growth.

Contribution

It derives an effective spin-1/2 XXZ Hamiltonian showing how trapping potentials strengthen nonergodic dynamics in strongly interacting regimes.

Findings

Trapping potential enhances nonergodicity even when weak.

Entanglement entropy grows logarithmically over time.

Effective Hamiltonian explains the trapping potential's role.

Abstract

We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state $|\psi(0)\rangle=|\cdots 2020\cdots \rangle$ 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 the hopping energy. We derive the effective spin-1/2 {\it 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.