Dynamical Behaviour of Density Correlations Across the Chaotic Phase for Interacting Bosons

TL;DR

This study analyzes how density correlations propagate in a one-dimensional Bose-Hubbard model, revealing ballistic and sub-ballistic regimes and detailing the effects of chaos on correlation spreading.

Contribution

It provides a detailed characterization of correlation transport across integrable and chaotic regimes, highlighting the emergence of long-time tails and amplitude decay effects.

Findings

Integrable limits show ballistic growth of correlation transport distance.

Chaotic phase induces a sub-ballistic regime with long-time tails.

Correlation front propagates ballistically across all interaction strengths.

Abstract

We investigate the propagation of two-point density correlations in the one-dimensional Bose-Hubbard Hamiltonian in the thermodynamic limit in terms of the correlation transport distance (CTD), an experimentally measurable magnitude that characterizes the spatial spreading of correlations in time. We confirm that the integrable limits of the model exhibit CTD ballistic growth, while the onset of the chaotic phase leads to the emergence of a pronounced sub-ballistic regime, in agreement with previous results for finite systems. By a meticulous analysis of the spatio-temporal correlation profiles, we show that the correlation front nonetheless propagates ballistically for all interaction strengths, and that the chaos-induced slowdown of the CTD originates from the emergence of long-time distance-dependent correlation tails, together with an enhanced decay of the correlation front amplitude. Our results thus provide a detailed characterization of correlation transport that goes beyond a simple light-cone picture.