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A system of coupled photonic cavities on a two-dimensional square lattice issystematically investigated using the stochastic series expansion quantum MonteCarlo method. The ground state phase diagram contains insulating phases withinteger polariton densities surrounded by a superfluid phase. The finite-sizescaling of the superfluid density is used to determine the phase boundariesaccurately. We find that the critical behavior is that of the generic,density-driven Mott-superfluid transition with dynamic exponent $z=2$, with nospecial multicritical points with $z=1$ at the tips of the insulating-phaselobes (as exist in the case of the Bose-Hubbard model). This demonstrates alimitation of the description of polaritons as structureless bosons.

Insulator to superfluid transition in coupled photonic cavities in two dimensions