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

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