  The quantum critical behavior of the Bose-Hubbard model for a description of
two coupled Bose-Einstein condensates is studied within the framework of an
algebraic theory. Energy levels, wavefunction overlaps with those of the Rabi
and Fock regimes, and the entanglement are calculated exactly as functions of
the phase parameter and the number of bosons. The results show that the system
goes though a phase transition and that the critical behavior is enhanced in
the thermodynamic limit.
