Extended Hubbard model

This note is organized as follows. In section II, the RVA is presented using the example of the two-legspin ladders. In section III, the RVA method is applied to the study of the dimerized chain described by the Extended Peierls-Hubbard model. A nice similarity between the two-leg ladder and this system is pointed out and comparisons with DMRG calculations are made. We conclude in section IV and give some reasonable perspectives. 

L.J. Dunne, E.J. Brandas, D-Wave Bipolaronic Condensate with Short Range Repulsive Electronic Correlations in an Extended Hubbard Model of High-Tc Cuprate Superconductors, Adv. Quant. Chem. 40 (2001) 225. 

The aim of this work is to demonstrate that the above-mentioned unusual properties of cuprates can be interpreted in the framework of the t-J model of a Cu-O plane which is a common structure element of these crystals. The model was shown to describe correctly the low-energy part of the spectrum of the realistic extended Hubbard model [4], To take proper account of strong electron correlations inherent in moderately doped cuprate perovskites the description in terms of Hubbard operators and Mori s projection operator technique [5] are used. The self-energy equations for hole and spin Green s functions obtained in this approach are self-consistently solved for the ranges of hole concentrations 0 < x < 0.16 and temperatures 2 K< T <1200 K. Lattices with 20x20 sites and larger are used. 

S. T. Chui and J. W. Bray, Computer renormalization group calculation of the 2kF and 4kF correlation functions of an extended one-dimensional Hubbard model, Phys. Rev. B21 1380-1384 (1983). 

Coulomb correlations In the PPP model automatically couple the ir and it subsystems even In the strict absence of ir-ir transfers. The same situation prevails In extended Hubbard models and the coupling becomes more Important when both subsystems have low-energy excitations. Such correlations have been neglected previously because, In the absence of ir-ir transfers, two subsystems merely change each other s self-consistent field. We expect previously studied ene-yne molecules to corroborate ir-ir coupling now that specific predictions can be tested. 

D-wave Bipolaronic Condensate with Short Range Reptdsive Electronic Correlations in an Extended Hubbard Model of High Tc Cuprate... 

The intra- and interchain Coulomb interactions between electrons on the TCNQ chains are the subject of extensive study. For a quarter filled band the on-site and nearest neighbour interactions 1 eV and 1 eV are considered in the framework of the extended Hubbard model. The interchain Coulomb... 

The extended Hubbard model discussed in reference 4 exhibits a superconducting instability when ... 

In the physics literature, the model invented to go beyond the severely truncated electron-repulsion range of the Hubbard model has been the extended Hubbard Hamiltonian or the U-V model. Here, the intersite interactions are introduced between bonded sites through another independent phenomenological interaction parameter V [26] from which the model derives its name. The Hamiltonian is given... 

In the context of NLO properties of interacting models such as the Hubbard and extended Hubbard models, it was shown by Soos and Rarnasesha that the model exact dyneimical NLO coefficients could be obtained by solving for correction vectors [106]. If we define the correction vector (u) by the equation... 

W. Barford, Excitons in the strong coupling limit of the one-dimensional extended Hubbard model, Phys. Rev. B 65 (2002) 205118. 

Jjl is the exchange integral responsible for an AF coupling (J > 0 in the present case). For an extended Hubbard model, it is necessary to use an effective Ugff [25] (instead of a bare U) which depends upon the band filling. 

One drastic consequence of this model is the decoupling of charge and spin excitations, with the appearance of an energy gap along the energy axis. There is a split of the initial electronic band into two (U effect), or more (V effect) sub-bands, which are separated by a Hubbard gap (Fig. 3). The value of this gap has been calculated for a 1-D extended Hubbard model [26]. 

These estimates, carried out in the atomic limit approximation of the extended Hubbard model, are, in principle, overestimated. Nevertheless, they confirm the general tendency U > 2V > 4 11 I, proposed by Mazumdar and Soos [59]. It must be also pointed out that the counter-ions, through their polarizability and shape, can modify the intrinsic U and V values [60]. 

One should also mention that a more realistic modeling of a quarter-filled system would require the inclusion of at least the nearest-neighbor Coulomb repulsion terms in addition to the on-site ones. That means switching from the original Hubbard to the extended Hubbard model Hamiltonian ... 

In the case of a long-range potential, or, more precisely, when the range of the potential is much larger than the range of the on-site wavefunctions, only the site-diagonal elements of the matrix of the interelectronic potential have to be retained in the model. Up to the first order in S, one ends up with the well Imown extended Hubbard model (EHM) ... 

An interesting possibility offered by the realization of the self-assembled crystals discussed above is to utilize them as floating mesoscopic lattice potentials to trap other particles, which can be atoms or polar molecules of a different species. We show below that within an experimentally accessible regime of parameters extended Hubbard models with tunable long-range phonon-mediated interactions describe the effective dynamics of the extra-particles dressed by the lattice phonons. 

The extended Hubbard model corresponding to the configuration of Eigure 12.1 la is characterized by tunable off-site interactions, which are a combination of the direct dipole-dipole interactions between the extra-particles and of the phonon-mediated interactions V-J Eor t>/a < 1/4 we find that the interactions decay slowly with... 

Ortner, M., Micheli, A., Pupillo, G., and Zoller, R, Quantum simulations of extended Hubbard models with dipolar crystals, 2009 (submitted for publication). 

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