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Abstract: Exact calculations of collective excitations and charge/spin (pseudo) gaps in an ensemble of bipartite and nonbipartite clusters yield level crossing degeneracies, spin-charge separation, condensation and recombination of electron charge and spin driven by interaction strength, inter-site couplings and temperature. Near crossing degeneracies, the electron configurations of the lowest energies control the physics of electronic pairing, phase separation and magnetic transitions. Rigorous conditions are found for the smooth and dramatic phase transitions with competing stable and unstable inhomogeneities. Condensation of electron charge and spin degrees at various temperatures offers a new mechanism of pairing and a possible route to superconductivity in inhomogeneous systems, different from the BCS scenario. Small bipartite and frustrated clusters exhibit charge and spin inhomogeneities in many respects typical for nano and heterostructured materials. The calculated phase diagrams in various geometries may be linked to atomic scale experiments in high cuprates, manganites and other concentrated transition metal oxides. [Copyright &y& Elsevier]

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 [ABSTRACT FROM AUTHOR]