Perturbative corrections to the Gutzwiller mean-field solution of the Mott-Hubbard model

TL;DR

This paper investigates how perturbative corrections refine the Gutzwiller mean-field approach to the Mott-insulator transition in bosonic optical lattices, improving the understanding of correlations and experimental observations.

Contribution

It introduces perturbative corrections to the Gutzwiller mean-field solution, enhancing the description of correlations and fluctuations near the Mott transition.

Findings

Corrections improve the description of number fluctuations and order parameter.

Short-range correlations in the one-particle density matrix are better captured.

Results are relevant for experimental expansion patterns in optical lattices.

Abstract

We study the Mott-insulator transition of bosonic atoms in optical lattices. Using perturbation theory, we analyze the deviations from the mean-field Gutzwiller ansatz, which become appreciable for intermediate values of the ratio between hopping amplitude and interaction energy. We discuss corrections to number fluctuations, order parameter, and compressibility. In particular, we improve the description of the short-range correlations in the one-particle density matrix. These corrections are important for experimentally observed expansion patterns, both for bulk lattices and in a confining trap potential.