“…For a fixed total occupation of a given site, the interaction J differentiates between the energies of different orbital occupation and spin states. In a lattice environment, this can lead to considerable shifts in the metal-Mott insulator phase boundaries [2,3], to local moment formation [4], nonlocal correlation effects [5,6], and various types of symmetry breaking [7][8][9][10][11][12][13]. Already in the two-band case, nontrivial crossovers and phase transitions can be observed.…”