The stationary properties of the Bose–Hubbard model under squeezed dissipation are investigated. The dissipative model does not possess aU (1) symmetry but conserves parity. We find that 〈a j 〉 = 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. As we increase the latter, 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 ansatz and the Gaussian Hartree–Fock–Bogoliubov approximation
