Correlation dynamics during a slow interaction quench in a one-dimensional Bose gas

TL;DR

This paper studies how a one-dimensional Bose gas's correlations evolve during a slow interaction increase, revealing distinct regimes of correlation decay and proposing a generalized light-cone framework.

Contribution

It introduces a comprehensive analysis of correlation dynamics during slow quenches, combining bosonization and DMRG methods, and proposes a generalized light-cone concept for diverse systems.

Findings

Short-distance correlations follow a power-law with distance.

Long-distance correlations decay algebraically, explained by a sudden quench approximation.

Intermediate regime exhibits stretched exponential decay of correlations.

Abstract

We investigate the response of a one-dimensional Bose gas to a slow increase of its interaction strength. We focus on the rich dynamics of equal-time single-particle correlations treating the Lieb-Liniger model within a bosonization approach and the Bose-Hubbard model using the time-dependent density-matrix renormalization group method. For short distances, correlations follow a power-law with distance with an exponent given by the adiabatic approximation. In contrast, for long distances, correlations decay algebraically with an exponent understood within the sudden quench approximation. This long distance regime is separated from an intermediate distance one by a generalized Lieb-Robinson criterion. At long times, in this intermediate regime, bosonization predicts that single-particle correlations decay following a stretched exponential. This latter regime is unconventional as, for one-dimensional interacting systems, the decay of single-particle correlations is usually algebraic within the Luttinger liquid picture. We develop here an intuitive understanding for the propagation of correlations, in terms of a generalized light-cone, applicable to a large variety of systems and quench forms.