Doorway states and the Bose-Hubbard model

TL;DR

This paper presents a doorway state method to efficiently solve the Bose-Hubbard model, accurately capturing many-body correlations and matching experimental and numerical results for 1D lattice systems.

Contribution

The paper introduces a doorway state approach that reduces computational complexity while accurately solving the Mott-Hubbard model.

Findings

Accurate calculation of chemical potential and on-site fluctuations.

Excellent agreement with numerical and experimental data.

Efficient reduction of Hilbert space dimensionality.

Abstract

We introduce an efficient method to solve the Mott-Hubbard model. The Schr\"{o}dinger equation is solved by the successive construction of doorway states. The ground state wavefunction derived by this method contains all relevant many-body correlations introduced by the hamiltonian, but the dimensionality of the Hilbert space is greatly reduced. We apply the doorway method to obtain the chemical potential, the on-site fluctuations and the visibility of the interference pattern arising from atoms in a one-dimensional periodic lattice. Excellent agreement with exact numerical calculations as well as recent experimental observations is found.