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arXiv:cond-mat/0412627 · physica status solidi (b)

Bound states in the phase diagram of the extended Hubbard model

M. Bąk

Published Jan 20, 2005• 4 citations
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Abstract

Abstract The paper shows how the known, exact results for the two electron bound states can modify the ground state phase diagram of extended Hubbard model (EHM) for on‐site attraction, intersite repulsion and arbitrary electron density. The main result is suppression of the superconducting state in favor of normal phase for small charge densities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200460049

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Abstract The paper shows how the known, exact results for the two electron bound states can modify the ground state phase diagram of extended Hubbard model (EHM) for on‐site attraction, intersite repulsion and arbitrary electron density. The main result is suppression of the superconducting state in favor of normal phase for small charge densities. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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Abstract The properties of the bound states on a lattice is an interesting problem related to the properties of superconductivity and Bose–Einstein condensation in a given model. By means of the exact solution of the Schrödinger equation the properties of the bound pairs on a frustrated, triangular lattice are examined within extended Hubbard model. Dispersion curves and mobilities are calculated for both positive and negative sign of the hopping integral. The possibility of increasing the mobility with increasing intersite Coulomb interaction is found. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abstract A refined variational wave function for the two‐dimensional repulsive Hubbard model is studied numerically, with the aim of approaching the difficult crossover regime of intermediate values of U. The issue of a superconducting ground state with d‐wave symmetry is investigated for an average electron density n ≈ 0.8 and for U = 8t. Due to finite‐size effects a clear‐cut answer to this fundamental question has not yet been reached. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
At weak coupling and at half filling, we analytically study effects of an intersite three-electron density interaction (P) of the one-dimensional extended Hubbard model in addition to the usual two-electron density interactions (U,V). By the bosonization and renormalization group approaches, we obtain the ground-state phase diagram of the model. In particular, we find that even in the presence of repulsive U and V, the attractive P may give rise to the superconducting phases for 2V≤min{2|P|;4|P|−U}.
Abstract We studied the quarter‐filled electron–hole Hubbard model of one dimension using the cluster perturbation method. We found that the ground states of this system are always insulating as long as the electron–hole attractive interaction has a finite value. The calculated density of states for the electron and hole is significantly renormalized by the interaction, and show energy gaps at the Fermi energy. These gaps are induced by the excitonic mechanism at U > U ′ and by the biexcitonic one at U < U ′, where U (> 0) denotes the electron–electron and hole–hole repulsive interaction, and U ′(< 0) denotes the electron–hole attractive interaction. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
By use of a diagrammatic method we determine the density-density response functions in the random-phase approximation (RPA) and the collective-excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state. The energy of the collective modes, given by the poles of these response functions, is found to be a linear function of the wave vector (for small k and short-range intersite interaction) with the velocity interpolating smoothly between the weak- (\ensuremath{\propto}2zt, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\ll}2zt) and strong-coupling (\ensuremath{\propto}zt2{\mathit{zt}}^{2}zt2/\ensuremath{\Vert}U\ensuremath{\Vert}, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}2zt) limits. The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong-coupling limit. The numerical analysis for a two-dimensional (2D) square lattice shows the occurrence of a rotonlike minima near the zone boundary. In the weak-coupling regime we find that apart from a commensurate charge-density-wave (CDW) instability, an increase in the intersite Coulomb repulsion can give rise to a CDW incommensurate with the lattice period, away from half-filling. The resulting phase diagram for the 2D square lattice, including a singlet superconducting ground state, electronic-droplet formation, and CDW's, is determined. Finally, the effects of a long-range Coulomb interaction are analyzed briefly and it is shown that the energy of collective excitations evolves smoothly from the weak- to the strong-coupling limit for a 2D lattice.