Nearest-Neighbor Tunneling Ansatz in the Bose-Hubbard Mode

TL;DR

This paper applies a recurrence-relation ansatz, previously used for the Jaynes-Cummings-Hubbard model, to the Bose-Hubbard model, simplifying its analysis and providing insights into two-point density correlations.

Contribution

It introduces a recurrence-relation ansatz for the Bose-Hubbard model, simplifying the analysis and potentially aiding in solving many-body quantum problems.

Findings

Two-point density correlations resemble previous results.

The ansatz simplifies the Bose-Hubbard model analysis.

Potential applicability to other many-body quantum systems.

Abstract

A recently introduced recurrence-relation ansatz applied to the Jaynes-Cummings-Hubbard model is here applied to the Bose-Hubbard model that reduced the model to an easily soluble model. The results obtained for the two-point density correlations resemble somewhat those obtained recently also but in a much more complicated fashion. Our ansatz may be of value for the solution of many-body quantum mechanical problems.