  We present a theoretical method to study driven-dissipative correlated
systems on lattices with two spatial dimensions (2D). The steady-state
density-matrix of the lattice is obtained by solving the master equation in a
corner of the Hilbert space. The states spanning the corner space are
determined through an iterative procedure, using eigenvectors of the
density-matrix of smaller lattice systems, merging in real space two lattices
at each iteration and selecting M pairs of states by maximizing their joint
probability. Accuracy of the results is then improved by increasing M, the
number of states of the corner space, until convergence is reached. We
demonstrate the efficiency of such an approach by applying it to the
driven-dissipative 2D Bose-Hubbard model, describing, e.g., lattices of coupled
cavities with quantum optical nonlinearities.
