Propagation front of correlations in an interacting Bose gas

TL;DR

This paper investigates the propagation of correlations in a one-dimensional Bose gas after a quench, identifying a propagation front velocity as a key characteristic to distinguish interaction regimes, and introduces analytical and numerical methods for analysis.

Contribution

It introduces a new approximation based on Jordan-Wigner fermionization for the Bose-Hubbard model and compares analytical results with numerical simulations across interaction strengths.

Findings

Propagation front velocity characterizes the many-body Hamiltonian.

Weak interactions are well described by free bosons.

Strong interactions involve quasiparticle pairs dominating dynamics.

Abstract

We analyze the quench dynamics of a one-dimensional bosonic Mott insulator and focus on the time evolution of density correlations. For these we identify a pronounced propagation front, the velocity of which, once correctly extrapolated at large distances, can serve as a quantitative characteristic of the many-body Hamiltonian. In particular, the velocity allows the weakly interacting regime, which is qualitatively well described by free bosons, to be distinguished from the strongly interacting one, in which pairs of distinct quasiparticles dominate the dynamics. In order to describe the latter case analytically, we introduce a general approximation to solve the Bose-Hubbard Hamiltonian based on the Jordan-Wigner fermionization of auxiliary particles. This approach can also be used to determine the ground-state properties. As a complement to the fermionization approach, we derive explicitly the time-dependent many-body state in the noninteracting limit and compare our results to numerical simulations in the whole range of interactions of the Bose-Hubbard model.