An exact study of charge-spin separation, pairing fluctuations and pseudogaps is carried out by combining the analytical eigenvalues of the four-site Hubbard clusters with the grand canonical and canonical ensemble approaches in a multidimensional parameter space of temperature (T ), magnetic field (h), on-site interaction (U ) and chemical potential (µ). Our results, near the average number of electrons N ≈ 3, strongly suggest the existence of a critical parameter Uc(T ) for the localization of electrons and a particle-hole binding (positive) gap ∆ e−h (T ) > 0 at U > Uc(T ), with a zero temperature quantum critical point, Uc(0) = 4.584. For U < Uc(T ), particle-particle pair binding is found with a (positive) pairing gap ∆ P (T ) > 0. The ground state degeneracy is lifted at U > Uc(T ) and the cluster becomes a Mott-Hubbard like insulator due to the presence of energy gaps at all (allowed) integer numbers (1 ≤ N ≤ 8) of electrons. In contrast, for U ≤ Uc(T ), we find an electron pair binding instability at finite temperature near N ≈ 3, which manifests a possible pairing mechanism, a precursor to superconductivity in small clusters. Rigorous criteria for the existence of many-body Mott-Hubbard like particle-hole and particle-particle pairings, spin-spin pairing, (spin) pseudogap and (spin) antiferromagnetic critical crossover temperatures, at which the corresponding pseudogaps disappear, are also formulated. In particular, the resulting phase diagram consisting of charge and spin pseudogaps, antiferromagnetic correlations, hole pairing with competing hole-rich ( N = 2), hole-poor ( N = 4) and magnetic ( N = 3) regions in the ensemble of clusters near 1/8 filling closely resembles the phase diagrams and inhomogeneous phase separation recently found in the family of doped high Tc cuprates.
Exact thermal studies of small (4-site, 5-site and 8-site)
Hubbard clusters with local electron repulsion yield intriguing insight into
phase separation, charge-spin separation, pseudogaps, condensation, in
particular, pairing fluctuations away from half filling (near optimal doping).
These exact calculations, carried out in canonical (i.e. for fixed electron
number N) and grand canonical (i.e. fixed chemical potential $\mu$) ensembles,
monitoring variations in temperature T and magnetic field h, show rich phase
diagrams in a T-$\mu$ space consisting of pairing fluctuations and signatures
of condensation. These electron pairing instabilities are seen when the onsite
Coulomb interaction U is smaller than a critical value U$_c$(T) and they point
to a possible electron pairing mechanism. The specific heat, magnetization,
charge pairing and spin pairing provide strong support for the existence of
competing (paired and unpaired) phases near optimal doping in these clusters as
observed in recent experiments in doped La$_{2-x}$Sr$_x$CuO$_{4+y}$ high T$_c$
superconductors.Comment: 5 pages, 5 figure
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