The two-state Bose-Hubbard model in the hard-core boson limit:   Non-ergodicity and the Bose-Einstein condensation
  The Bose-Einstein condensation in the hard-core boson limit (HCB) of the Bose-Hubbard model with two local states and the particle hopping in the excited band only is investigated. For the purpose of considering the non-ergodicity, a single-particle spectral density is calculated in the random phase approximation by means of the temperature boson Green functions. The non-ergodic contribution to the momentum distribution function of particles (connected with the static density fluctuations) increases significantly and becomes comparable with the ergodic contribution in the superfluid phase near the tricritical point. 
I. V. Stasyuk, O. V. Velychko
cond-mat.quant-gas