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An exact study of charge-spin separation, pairing fluctuations and pseudogapsis carried out by combining the analytical eigenvalues of the four-site Hubbardclusters with the grand canonical and canonical ensemble approaches in amultidimensional parameter space of temperature (T), magnetic field (h),on-site interaction (U) and chemical potential. Our results, near the averagenumber of electrons <N>=3, strongly suggest the existence of a criticalparameter U_{c}(T) for the localization of electrons and a particle-holebinding (positive) gap at U>U_{c}(T), with a zero temperature quantum criticalpoint, U_{c}(0)=4.584. For U<U_{c}(T), particle-particle pair binding is foundwith a (positive) pairing gap. The ground state degeneracy is lifted atU>U_c(T) and the cluster becomes a Mott-Hubbard like insulator due to thepresence of energy gaps at all (allowed) integer numbers of electrons. Incontrast, for U< U_c(T), we find an electron pair binding instability at finitetemperature near <N>=3, which manifests a possible pairing mechanism, aprecursor to superconductivity in small clusters.  In addition, the resulting phase diagram consisting of charge and spinpseudogaps, antiferromagnetic correlations, hole pairing with competinghole-rich (<N>=2), hole-poor (<N>=4) and magnetic (<N>=3) regions in theensemble of clusters near 1/8 filling closely resembles the phase diagrams andinhomogeneous phase separation recently found in the family of doped high T_ccuprates.Comment: 10 pages, 7 figure

Exact study of charge-spin separation, pairing fluctuations, and pseudogaps in four-site Hubbard clusters