Suppressed correlation-spreading in a one-dimensional Bose-Hubbard model with strong interactions

TL;DR

This paper studies non-ergodic behavior and suppressed correlation spreading in a strongly interacting one-dimensional Bose-Hubbard model, revealing slow dynamics, localized correlations, and effects of trapping, with a mapping to an effective spin model.

Contribution

It demonstrates how strong interactions lead to suppressed correlation spreading and slow relaxation, and maps the Bose-Hubbard model to an antiferromagnetic spin model for analysis.

Findings

Correlation spreading is suppressed at strong interactions.

Domain wall excitations dominate the dynamics.

Trap edges further inhibit correlation propagation.

Abstract

We investigate signatures of non-ergodic behavior in the real-time evolution of a one-dimensional Bose-Hubbard model, where the initial state is a doubly occupied density-wave state. We show that the occupation dynamics at strong interactions is dominated by doublon-holon exchange which leads to a domain wall excitation and propagation. The latter manifests as a negated staggered pattern in the density-density correlations. While the single-particle and the pair correlation functions show highly localized correlations that decay rapidly away from the nearest neighbor. We show that the time scale of the domain-wall excitations depends on the inverse of the interaction strength and therefore dictates the slow relaxation dynamics. In the presence of a parabolic trap, the occupation dynamics at the edges become frozen and further suppresses the propagation of correlations. This suppression happens even for trap strengths weaker than the tunneling rate. We also show that the model can be mapped to an antiferromagnetic transverse-field Ising model in the limit of strong interactions and that the correlation-propagation velocity in the original model is well captured by the group velocity of the spin-wave excitation in the effective spin model.