Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model

TL;DR

This paper studies how correlations and entanglement spread in a one-dimensional Bose-Hubbard model after a sudden quench, revealing light-cone like dynamics and their relation to system velocities and phase transitions.

Contribution

It provides a detailed analysis of the spreading of correlations and entanglement post-quench, linking velocities to system properties and phase transitions.

Findings

Correlations and entanglement spread with a finite velocity resembling a light cone.

Von-Neumann entropy grows rapidly, while mutual information can decrease after initial increase.

Static von-Neumann entropy indicates the quantum phase transition location.

Abstract

We investigate the spreading of information in a one-dimensional Bose-Hubbard system after a sudden parameter change. In particular, we study the time-evolution of correlations and entanglement following a quench. The investigated quantities show a light-cone like evolution, i.e. the spreading with a finite velocity. We discuss the relation of this veloctiy to other characteristic velocities of the system, like the sound velocity. The entanglement is investigated using two different measures, the von-Neuman entropy and mutual information. Whereas the von-Neumann entropy grows rapidly with time the mutual information between two small subsystems can as well decrease after an initial increase. Additionally we show that the static von Neuman entropy characterises the location of the quantum phase transition.