Exact thermodynamics of pairing and charge-spin separation in Hubbard nanoclusters

An exact thermal studies of charge-spin separation, pairing fluctuations and pseudogaps are carried out by exact diagonalization of 4-site, frustrated (three dimensional) tetrahedral Hubbard and planar (2x4) clusters. Our exact results for 4-site cluster strongly suggest the existence of a quantum critical points in small Hubbard clusters for particle-particle/hole pair binding, antiferromagnetism, unsaturated and saturated ferromagnetism. Exact studies of larger planar and three dimensional Hubbard clusters yield more intriguing insight supporting the analytical results obtained for the 4-site clusters. Our microscopic theory reproduces electron pairing correlations, phase separation and magnetism in clusters, small nanoparticles, and, surprisingly, in transition metal oxides and high T$_c$ doped cuprates. Theory describes also the effect of pressure on the superconducting transition temperature, the presence of a dormant magnetic state in a narrow region of doping and variation of spin pseudogap with doping level, etc.