Multiband Effects and the Bose-Hubbard Model in One-Dimensional Lattices

TL;DR

This paper investigates the phase transitions of one-dimensional bosonic systems in lattices, comparing continuous-space simulations with the Bose-Hubbard model, and introduces a scattering analysis to improve model accuracy for strong interactions.

Contribution

It reveals the limitations of the one-band Bose-Hubbard model for strong interactions and proposes an inverse scattering method to accurately determine model parameters.

Findings

Breakdown of one-band approximation for strong interactions.

Inverse scattering analysis yields correct $U/J$ ratios.

Bose-Hubbard model matches continuous results with proper parameters.

Abstract

We study phase diagrams of one-dimensional bosons with contact interactions in the presence of a lattice. We use the worm algorithm in continuous space and focus on the incommensurate superfluid Mott-insulator transition. Our results are compared to those from the one-band Bose-Hubbard model. When Wannier states are used to determine the Bose-Hubbard model parameters, the comparison unveils an apparent breakdown of the one-band description for strong interactions, even for the Mott-insulating state with an average of one particle per site ($n=1$) in deep lattices. We introduce an inverse confined scattering analysis to obtain the ratio $U/J$, with which the Bose-Hubbard model provides correct results for strong interactions, deep lattices, and $n=1$.