Many-Polaron Theory for CDW, SDW and Superconducting Phases in One-Dimensional N-Sites N-Elctrons System –Quantum-Classic Crossover–

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Abstract
A one-dimensional many-electron system with on-site electron-electron(e-e) and electron-phonon(e-p) interactions is studied in the context of polaron theory, so as to clarify the quantum effect of phonon on the phase diagram. Lattice distortions moving with electrons as well as a frozen one are taken into account by a variational method combined with mean field theory. The phase diagram is given in a tetrahedral coordinate, spanned by four parameters : inter-site transfer of electron T , e-e repulsion U , e-p coupling S and phonon energy ω. This “T-U-S-ω tetrahedron” is shown to be divided into CVW and SDW regions by the boundary S = U . In the CDW region, the polaron radius increases as the retardation effect increases, and in its long limit the superconducting state(SCS) becomes far unstable than CDW, while in its short limit, SCS is degenerate with CDW, indicating the importance of this radius in quantum-classic crossover.