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arXiv:0912.4137 · The European Physical Journal B

Different orderings in the narrow-band limit of the extended Hubbard model on the Bethe lattice

F. Mancini, F. P. Mancini

Published Jan 27, 2010• 7 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2010-00031-8

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We study the influence of an external magnetic field h on the phase diagram of a system of Fermi particles living on the sites of a Bethe lattice with coordination number z and interacting through on-site U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the narrow-band limit. Our results establish that the magnetic field may dramatically affect the critical temperature below which a long-range charge ordered phase is observed, as well as the behavior of physical quantities, inducing, for instance, magnetization plateaus in the magnetization curves. Relevant thermodynamic quantities - such as the specific heat and the susceptibility - are also investigated at finite temperature by varying the on-site potential, the particle density and the magnetic field.
The variation of the superconducting order parameter (extended s wave) with hole concentration is studied for a narrow-band system, described by an extended Hubbard model, using the renormalized Hamiltonian approach (RHA) and X-operator technique in the strong-correlation limit and by the Hartree-Fock approximation for the weak correlation case. A comparison of the results obtained by using the RHA and the X-operator technique are made for different densities of states. Analytical results for the superconducting order parameter and its relation to the delocalization energies in the normal and superconducting states are obtained at zero chemical potential.
The extended Hubbard model with the pair-hopping interaction, i.e. the Penson-Kolb-Hubbard model, is one of the conceptually simplest phenomenological models for studying correlations and for description of superconductivity in very narrow-band systems with short-range, almost unretarded pairing.We present ground state phase diagrams of the model derived within the broken-symmetry Hartree-Fock approximation in the narrow-bandwidth regime and compare these results with the exact ones in the atomic limit for the limit of high dimensions.The investigation of the diagrams of the model show that results obtained within both approaches are consistent, although for the case of the finite single-electron hopping phases with magnetic long-range order also occur.