Solution of one-dimensional Bose Hubbard model in large-$U$ limit

TL;DR

This paper exactly solves the one-dimensional Bose-Hubbard model in the large-U limit by mapping it to a simpler Hamiltonian, deriving eigenstates, eigenvalues, and thermodynamic properties, and developing a new perturbation approach.

Contribution

It provides an exact solution for eigenstates and eigenvalues in fixed occupancy subspaces and introduces a novel perturbation method for the large-U regime.

Findings

Eigenstates and eigenvalues obtained exactly for fixed occupancy subspaces

Thermodynamic properties calculated explicitly

Ground-state energy derived to first order in 1/U

Abstract

The one-dimensional Bose-Hubbard model in large-$U$ limit has been studied via reducing and mapping the Hamiltonian to a simpler one. The eigenstates and eigenvalues have been obtained exactly in the subspaces with fixed numbers of single- and double-occupancies but without multiple-occupancies, and the thermodynamic properties of the system have been calculated further. These eigenstates and eigenvalues also enable us to develop a new perturbation treatment of the model, with which the ground-state energy has been calculated exactly to first order in $1/U$.