Dynamic density-density correlations in interacting Bose gases on optical lattices

TL;DR

This paper investigates the dynamic density-density correlations in one-dimensional interacting Bose gases on optical lattices, identifying signatures of the superfluid to Mott-insulator transition through advanced numerical and analytical methods.

Contribution

It provides a detailed analysis of the charge structure factor using DDMRG and compares results with strong-coupling expansion and mean-field theory, highlighting phase transition signatures.

Findings

Strong-coupling expansion accurately reproduces DDMRG results in Mott phase.

Linear excitation spectrum near zero momentum in superfluid phase identified.

Behavior of charge structure factor varies distinctly across the phase transition.

Abstract

In order to identify possible experimental signatures of the superfluid to Mott-insulator quantum phase transition we calculate the charge structure factor $S(k,\omega)$ for the one-dimensional Bose-Hubbard model using the dynamical density-matrix renormalisation group (DDMRG) technique. Particularly we analyse the behaviour of $S(k, \omega)$ by varying---at zero temperature---the Coulomb interaction strength within the first Mott lobe. For strong interactions, in the Mott-insulator phase, we demonstrate that the DDMRG results are well reproduced by a strong-coupling expansion, just as the quasi-particle dispersion. In the superfluid phase we determine the linear excitation spectrum near $k=0$ and compare the DDMRG data with results from mean-field theory.