Phase separation instabilities and magnetism in two dimensional square and honeycomb Hubbard model

The variational cluster approximation is applied to rigorously calculate intrinsic local electron correlations in bipartite square and honeycomb Hubbard lattices. The Mott–Hubbard gap at half filling is manifested by a smooth metal–insulator transition in both lattices in agreement with the generic two-dimensional phase diagram. However, a density variation with the chemical potential shows the distinct structural differences away from half filling. The square lattice exhibits electron density discontinuity accompanied with spontaneous transition from antiferromagnetic Mott–Hubbard insulator into nonmagnetic metal. The spectral density anomaly and spin susceptibility peaks also are signaling on coexistence of hole rich metallic and hole poor insulating regions. In contrast, honeycomb lattice does not show density anomaly but displays a smooth transition with continuous evolution of a homogenous metallic state. These calculations provide strong evidence for spontaneous phase separation instability found in our quantum cluster calculations at moderate U •Variational cluster approximation (VCA) captures phase separation in various lattices under doping.•The conditions are formulated for continuous and discontinuous transitions.•Discontinuous phase separation is found in square lattices under doping and pressure.•Honeycomb lattice displays continuous evolution of a homogenous metallic state.•Spectral function anomaly in square geometry displays the folding of the first Brillouin zone.