Propagation of quantum correlations after a quench in the Mott-insulator regime of the Bose-Hubbard model

TL;DR

This paper investigates the dynamics of quantum correlations in the Bose-Hubbard model after a sudden quench from a Mott insulator to a finite tunneling regime, using a reduced density matrix approach to simulate large systems.

Contribution

It introduces a numerical method that approximates many-body quantum dynamics by neglecting higher-order correlations, enabling simulation of large lattice systems after a quench.

Findings

Captured the light-cone spreading of correlations.

Simulated dynamics for around 1000 lattice sites.

Provided insights into non-equilibrium quantum correlation propagation.

Abstract

We study a quantum quench in the Bose-Hubbard model where the tunneling rate $J$ is suddenly switched from zero to a finite value in the Mott regime. In order to solve the many-body quantum dynamics far from equlibrium, we consider the reduced density matrices for a finite number (one, two, three, etc.) of lattice sites and split them up into on-site density operators, i.e., the mean field, plus two-point and three-point correlations etc. Neglecting three-point and higher correlations, we are able to numerically simulate the time-evolution of the few-site density matrices and the two-point quantum correlations (e.g., their effective light-cone structure) for a comparably large number ${\cal O}(10^3)$ of lattice sites.