  We investigate steady-state properties of a two-dimensional incoherent-pumped
dissipative Bose-Hubbard model, which describes a photon square lattice. This
incoherent pumping exhibits an important environment-induced higher-order
fluctuation effect, which induces a strong competition between the
driven-dissipative channel, the photon-photon interaction, and the photon
hopping in multi-photon processes. This new competition gives rise to a
spontaneous breaking of the U(1) symmetry of system. As a result, we predict a
many-body steady-state localized-delocalized phase transition and an
anti-blockade effect, in which the increasing of the repulsive photon-photon
interaction promotes the emergence of phase transition. These unconventional
many-body steady-state phenomena can be understood by analyzing the
single-cavity properties. Our results pave a new way to control many-body
dynamics of driven-dissipative systems.
