One-band Hubbard model

Among numerous theoretical approaches, the Gutzwiller method [11,12] provides a transparent physical interpretation in term of atomic configurations of a given site. Originally it was applied to the one-band Hubbard model Hamiltonian [13] ... 

The purpose of these notes is to show how some strongly correlated electron models like the one-band Hubbard model with infinite electron repulsion on rectangular and triangular lattices can be described in terms of spinless fermions and the operators of cyclic spin permutations. We will consider in detail the... 

Fig. 3. The < tical conductivity calculated within a one-band Hubbard model on a 4x4 cluster (Dagotto 1994). Parameter x stands for the hole-doping fraction. Calculations reproduce the principal trends of the experimental data on the evolution of the electromagnetic response with doping. In particular, theoretical spectra reveal (i) the transfer of the spectral weight from the CT excitation to the iow-ftequency region (ii) development of mid-infiared absorption at light doping (x = 0.125) and (iii) growth of the Drude-like feature at higher dopings (x > 0.2). Note that the isobestic point at m/t = 5 is also reproduced.

The three-band model has several parameters and is still rather complicated. Therefore, an even simpler model, the one-band Hubbard model, is often used as a crude model for high Tq materials. The Hubbard model arranges the tight-binding states on a square lattice. Each electron can hop to a nearest-neighbor site and two electrons (of different spin) on the same site have a repulsive interaction. No other electron-electron interactions are included therefore the Hubbard model assumes the repulsions are heavily screened by the ions in the crystal. There have been attempts to justify the reduction of the three-band model to the one-band Hubbard model, although the justifications must be considered very weak. Therefore, the one-band Hubbard model would not describe the details of high Tq materials correctly, but at best qualitatively. 

Another model which is widely used for the description of Cu-0 planes of cuprates is the one-band Hubbard model with the Hamiltonian... 

Mori s projeetion operator formalism and the strong-coupling diagram technique, the t-J and the one-band Hubbard models of Cu-0 planes were used for the interpretation of the... 

Figure 11 1 2. The Bom effective charge of oxygen calculated for the one-dimensional two-band Hubbard model with the Cu-0 bond-stretching LO mode, calculated for N = 12 ring with doping level x = 0, 1/3 and for N = 16 ring with x = 0, 1/4. The dashed line correspond to the static (ionic) charge [12]...

What is a minimum model for describing the main physics of a single Q1O2-plane In this paper we employ an effective one-band Hubbard Hamiltonian ... 

The single-band ladder extension of the one-dimensional Hubbard model [18,19,22] has been utilized as a minimalist model to smdy spin-liquid behavior [11, 14, 43] and high-temperature superconductors [1, 5, 21, 25, 44]. The ladder model is a quasi-one-dimensional system with a fourfold degenerate Fermi surface and correlations in two-dimensions. 

We have discussed, in Chap. A, the Hubbard model for localization vs. itineracy in narrow bands. In this model, it was shown, for a simple case ( hydrogen case) involving one uncoupled electron in a shell, that a splitting of the narrow band in two sub-bands occurs when the Hubbard condition (Uh = W) is not satisfied. The two sub-bands describe two situations ... 

Figure 15 (a) One-band model where electrons are removed from the lower Hubbard band on doping, (b) One-band model where electrons are removed from the tr band of the material on doping, (c) Similar to (b) but where the system is a normal metal described by (W/U) > (W/U)crit of Figure 11. 

Electron correlation plays an important role in determining the electronic structures of many solids. Hubbard (1963) treated the correlation problem in terms of the parameter, U. Figure 6.2 shows how U varies with the band-width W, resulting in the overlap of the upper and lower Hubbard states (or in the disappearance of the band gap). In NiO, there is a splitting between the upper and lower Hubbard bands since IV relative values of U and W determine the electronic structure of transition-metal compounds. Unfortunately, it is difficult to obtain reliable values of U. The Hubbard model takes into account only the d orbitals of the transition metal (single band model). One has to include the mixing of the oxygen p and metal d orbitals in a more realistic treatment. It would also be necessary to take into account the presence of mixed-valence of a metal (e.g. Cu ", Cu ). 

Likewise the Hubbard model the periodic Anderson model (PAM) is a basic model in the theory of strongly correlated electron systems. It is destined for the description of the transition metals, lanthanides, actinides and their compositions including the heavy-fermion compounds. The model consists of two groups of electrons itinerant and localized ones (s and d electrons), the hybridization between them is admitted. The model is described by the following parameters the width of the s-electron band W, the energy of the atomic level e, the on-site Coulomb repulsion U of d-electrons with opposite spins, the parameter V of the... 

Quite recently the ferromagnetic ground state in a class of Hubbard systems on decorated lattices that contain flat or nearly flat lowest energy bands has been found [42,43]. Obviously such multiband systems have more degrees of freedom than the one-band model considered by Nagaoka, and we can expect the appearance of unusual effects even in the case of infinite electron repulsion. 

As a result we have obtained the effective Hamiltonian with the two types of interaction of neighboring segments. The competition between these types of interactions leads to the formation of a magnetic polaron similar to the anisotropic one band U=oo Hubbard model. 

One of the simple models of high-Tc superconducting copper oxides is a two-band Hubbard Hamiltonian (so called Emery model) [46]... 

To cover the gap between them the Hubbard model Hamiltonian was quite generally accepted. This Hamiltonian apparently has the ability of mimicking the whole spectrum, from the free quasi-particle domain, at U=0, to the strongly correlated one, at U —> oo, where, for half-filled band systems, it renormalizes to the Heisenberg Hamiltonian, via Degenerate Perturbation Theory. Thence, the Heisenberg Hamiltonian was assumed to be acceptable only for rather small t/U values. 

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