Superfluidity of the Bose-Hubbard model: su(1,1) linearization scheme

Statistical mechanics of the bosonic Hubbard model is studied in the frame of an improved linearization scheme, applied in such a way so as to approximate in thermodynamically self-consistent way the local interaction and keeping all long-range correlations exact in the linearized form. The hamiltonian spectrum can be obtained due to the resulting dynamical symmetry, and the self-consistent free energy allows us to obtain the temperature dependence of the diagonal and off-diagonal order parameters. The phase diagram exhibits a superfluid condesate phase possibly co-existing, for appropriate values of (U/t)ν, with a fluctuation-mediated off-diagonal long-range-ordered phase. The corresponding transition can be thought of as a conductor-insulator transition.