Possible phase separation in square and honeycomb Hubbard model: A variational cluster study

•VCA study of possible spontaneous phase separation in 2D square and honeycomb Hubbard lattices.•Phase separation instabilities and density inhomogeneities driven by proximity to level crossing.•Contrasting differences in behaviors of spectral functions in square and honeycomb near first Brillouin zone.•VCA strongly confirms spontaneous phase separation obtained at level crossings in cluster calculations.

The VCA ground state of the 2D Hubbard model is examined for possible phase separation under hole doping manifested by spatial inhomogeneities of coexisting different electron densities at equilibrium. Phase separation is accompanied by spectral weight loss and first Brillouin zone boundary deformation. Such an instability is observed in square structures and it is absent in honeycomb lattices. To our knowledge, no previous publications have revealed relationship between a Fermi surface instability and phase separation. Our VCA calculations provide strong support for this spontaneous instability, driven by electron correlations in specific lattice geometries, proposed in our earlier publications using exact quantum cluster calculations.