Extended Hubbard Hamiltonian model

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... 

An intriguing possibility is offered by the interaction engineering discussed above in the context of the realization of effective lattice models where particles interact via exotic (extended) Hubbard Hamiltonians. An example of this is given in Ref. [85], where it is shown how to engineer the following Hubbard-like Hamiltonian... 

The magnetic susceptibility measurements allow a determination of the Hubbard U value. From the magnetic data [489] has been estimated 17/4/ in 2-chain compounds such as TTF-TCNQ. This approach has been generalized in [490]. The authors of these papers used an extended Hubbard Hamiltonian and they showed that the magnetic susceptibility varies strongly and systematically as a function of band filling. An important result shows that the extended Hubbard data cannot be mapped systematically onto the results of a Hubbard model with an effective U value. 

The properties of low-dimensional organic conductors are determined by different interactions and instabilities (see, e.g., Chapter 2). It is commonly assumed that it can be treated as in ordinary metals with a frozen long-range interaction part, while the short-range part gives rise to quasiparticles with screened interactions. Thus the proper model Hamiltonian is of the extended Hubbard type [11]. 

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 ... 

Hiickel and PPP theory emphasize common aspects of 7T electrons in molecules whose geometry is specified in advance. The backbones of the representative conjugated polymers in Fig. 6.2, for example, immediately fix the Hiickel or PPP Hamiltonians. Effects due to substituents R or sulfur heteroatoms in polythiophene (PT) are approximated by site energies or neglected as perturbations of TT-TT tran.sitions. Such a priori information about Ha and V(/ ) comes from molecules and contrasts sharply with the adjustable parameters of extended Hubbard models. The a- conjugation encountered in polysi-... 

The vibrational consequences of 7r-electron fluctuations discussed in Sections II and III drew on both molecular spectroscopy and solid-state physics. The analysis of NLO and EA spectra in Section IV combined PPP models for molecules with quantum cell models of alternating chains. We proposed at the outset to relate the conjugated polymers in Fig. 6.2 to alternating Fliickel or PPP chains and have so far discussed vibrational and optical implications of 7r-electron models rather than the Hamiltonian, Eq. (7), or its mathematical properties. The analysis holds for any H(8) with appropriate vibrational or optical susceptibilities. Equation (7) is sufficiently general to encompass Hiickel, Hubbard, extended Hubbard, PPP, and other models with suitable choices of U and Vp,. This generality is an extremely useful feature of solid-state models. 

The two-dimensional t-J model was shown to describe correctly the low-energy part of the spectrum of the extended Hubbard model, which gives a realistic description of the Cu-0 plane of cuprates [46-48]. The Hamiltonian of the t-J model reads... 

---