Phase and group velocities for correlation spreading in the Mott phase of the Bose-Hubbard model in dimensions greater than one

TL;DR

This paper calculates and compares phase and group velocities for correlation spreading in the Bose-Hubbard model across multiple dimensions, confirming experimental observations and demonstrating the effectiveness of the 2PI strong coupling approach.

Contribution

It introduces a 2PI strong coupling method to accurately compute correlation velocities in the Bose-Hubbard model in higher dimensions, aligning with experimental data.

Findings

Quantitative agreement with experimental velocities in 1D and 2D.

Phase velocity can significantly differ from group velocity.

Anisotropy in correlation spreading varies across the phase diagram.

Abstract

Lieb-Robinson and related bounds set an upper limit on the rate of spreading of information in non-relativistic quantum systems. Experimentally, they have been observed in the spreading of correlations in the Bose-Hubbard model after a quantum quench. Using a recently developed two particle irreducible (2PI) strong coupling approach to out-of-equilibrium dynamics in the Bose-Hubbard model we calculate both the group and phase velocities for the spreading of single-particle correlations in one, two and three dimensions as a function of interaction strength. Our results are in quantitative agreement with measurements of the velocities for the spreading of single particle correlations in both the one and two dimensional Bose-Hubbard model realized with ultra-cold atoms. They also agree with the claim that the phase velocity rather than the group velocity was observed in recent experiments in two dimensions. We demonstrate that there can be large differences between the phase and group velocities for the spreading of correlations and also explore the variation of the anisotropy in the velocity at which correlations spread across the phase diagram of the Bose-Hubbard model. Our results establish the 2PI strong coupling approach as a powerful tool to study out-of-equilibrium dynamics in the Bose-Hubbard model in dimensions greater than one.