  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.
