Hubbard parameter

We demonstrate some of the ideas for a vTS x /T8 Hubbard lattice containing 18 electrons, with periodic boundary conditions. This model has been extensively studied [11]. The Hubbard parameter was set to U/t = 4. The ground-state of the non-interacting system, being diagonalised by plane-waves, is a closed shell consisting of l- -4- -4 doubly occupied levels. There are 2M = 36 one particle orbtials, leading to Ndet = 9075135300 determinants for an... 

The Hubbard parameter can be approximated by the difference of the ionization potential and the electron affinity of the atom. 

An interpretation of apactroacopic data for the hitfh temperature superconductors utilizing a highly correlated CuOm cluster model shows that a single set of Hubbard parameters predicts all of the state energies. Differences in the data from that for CuO are attributed to an increased Cu-0 covalency in the superconductors. The reported temperature effects are attributed to increased metallic screening at lower temperatures. 

Table 1 contains the estimates of the Hubbard parameters which together provide the best agreement with the state energies as reflected in the spectra and the theoretical DOS. The energies relative to the ground state are given in terms of the Hubbard g and U parameters defined above. The agreement of the estimated energies with the spectral features is also shown in Table 1. We discuss the assignment of the spectral features below.

TABLE 1 Summary of hole states revealed in the spectroscopic data, and estimated energies using the following optimal values for the Hubbard parameters in eV> ... 

The Cu L VV and LttMiaV Auger data (9,33,41-43) reflect the v and cv DOS, respectively, and therefore provide further information on the Hubbard parameters. The Lt and Lt features and associated satellites are identified in Fig. 3. Table 1 indicates that the energies of these features are predicted accurately by the U and c parameters established above. We need only discuss the relative intensities. 

The tunability of the lattice allows access to a wide range of Hubbard parameters and phonon couplings. Compared with optical lattices, for example, a small-scale lattice yields significantly enhanced hopping amplitudes, which set the relevant energy scale... 

FIGURE 12.12 Configuration 1 (Figure 12.11a) Hubbard parameters for d /dc = 0.1 and m = nip. (a) Lattice depth Vq in units of vs. b/a for = 50 and 500. Thick continuous lines tight-binding region 47 < A. (b) Reduction factor Sq (dashed-dotted lines) and polaron shift Ep/J (solid lines), for 47 < A. (c) Continuous lines phonon-mediated... 

Here we have introduced Ur as the Hubbard parameter for the energy of interaction between two electrons residing on the same site. 

A complementary point, following this analysis, is the hierarchy of the electronic correlations and the electron-phonon interactions. In the presence of extended 7r-systems, U and V Hubbard parameters decrease and they become about the same order of magnitude as the interactions with the phonon lattice and molecular vibrations. In such a situation a polaronic process occurs even the case of bipolarons associated with a two electron transfer has been predicted with the possible occurrence of a Bose condensation [333a]. 

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