  The stationary properties of the Bose-Hubbard model under squeezed
dissipation are investigated. The dissipative model does not possess a $U(1)$
symmetry, but parity is conserved: $\langle a_j \rangle \to -\langle a_j
\rangle$. We find that $\langle a_j \rangle = 0$ always holds, so no symmetry
breaking occurs. Without the onsite repulsion, the linear case is known to be
critical. At the critical point the system freezes to an EPR state with
infinite two mode entanglement. We show here that the correlations are rapidly
destroyed whenever the repulsion is switched on. Then, the system approaches a
thermal state with an effective temperature defined in terms of the squeezing
parameter in the dissipators. We characterize this transition by means of a
Gutzwiller {\it ansatz} and the Gaussian Hartree-Fock-Bogoliubov approximation.

Statistical Mechanics;Quantum Physics