Bosons Confined in Optical Lattices: the Numerical Renormalization Group revisited

TL;DR

This paper revisits the study of bosons in optical lattices using an improved variational method combining Gutzwiller mean-field and Numerical Renormalization Group techniques, providing detailed results across multiple dimensions.

Contribution

It introduces a hybrid MF+NRG approach that enhances the analysis of the Bose-Hubbard model in optical lattices, especially in capturing momentum distributions.

Findings

Accurate momentum distribution predictions for 1D, 2D, and 3D systems.

Comparison with exact results in 1D validates the method.

Identification of satellite peaks in momentum distributions.

Abstract

A Bose-Hubbard model, describing bosons in a harmonic trap with a superimposed optical lattice, is studied using a fast and accurate variational technique (MF+NRG): the Gutzwiller mean-field (MF) ansatz is combined with a Numerical Renormalization Group (NRG) procedure in order to improve on both. Results are presented for one, two and three dimensions, with particular attention to the experimentally accessible momentum distribution and possible satellite peaks in this distribution. In one dimension, a comparison is made with exact results obtained using Stochastich Series Expansion.