Propagation of a single hole defect in the one-dimensional Bose-Hubbard model

TL;DR

This paper investigates the nonequilibrium dynamics of a single hole defect in the 1D Bose-Hubbard model, revealing ballistic and diffusive propagation modes near the quantum critical point and contrasting global quench with ground state dynamics.

Contribution

It introduces an effective fermionic model to explain the ballistic mode as interference between holon and doublon dynamics, and compares global quench to ground state dynamics in detail.

Findings

Ballistic mode velocity matches maximum doublon dispersion slope.

Near the critical point, the hole splits into slow diffusive and fast ballistic components.

Entanglement entropy grows faster in global quench than in ground state dynamics.

Abstract

We study nonequilibrium dynamics in the one-dimensional Bose-Hubbard model starting from an initial product state with one boson per site and a single hole defect. We find that for parameters close to the quantum critical point, the hole splits into a core showing a very slow diffusive dynamics, and a fast mode which propagates ballistically. Using an effective fermionic model at large Hubbard interactions U, we show that the ballistic mode is a consequence of an interference between slow holon and fast doublon dynamics, which occurs once the hole defect starts propagating into the bosonic background at unit filling. Within this model, the signal velocity of the fast ballistic mode is given by the maximum slope of the dispersion of the doublon quasiparticle in good agreement with the numerical data. Furthermore, we contrast this global quench with the dynamics of a single hole defect in the ground state of the Bose-Hubbard model and show that the dynamics in the latter case is very different even for large values of U. This can also be seen in the entanglement entropy of the time evolved states which grows much more rapidly in time in the global quench case.