Fermi hole hamiltonian

It is clear that, for electrons with parallel spins, the auxiliary condition (Eq. II.2) gives rise to a correlation effect which very closely resembles the correlation effect coming from the Coulomb repulsion in the Hamiltonian for = 2 the Fermi hole replaces to a certain degree the Coulomb hole. This means that, if... 

This effect is known as exchange or Fermi correlation and is a direct consequence of the Pauli principle. The Fermi hole is in no way connected to the charge of electrons and applies equally to neutral fermions. This kind of correlation is included in the HF appro ich due to the antisymmetry of the Slater determinant [337]. The electrostatic repulsion of electrons (the l/ri2 term in the Hamiltonian) prevents the electrons from coming too close to each other and is known as Coulomb correlation. This effect is independent of the spin and is called simply electron correlation, and is completely neglected in the HF method. 

The ZSA phase diagram and its variants provide a satisfactory description of the overall electronic structure of stoichiometric and ordered transition-metal compounds. Within the above description, the electronic properties of transition-metal oxides are primarily determined by the values of A, and t. There have been several electron spectroscopic (photoemission) investigations in order to estimate the interaction strengths. Valence-band as well as core-level spectra have been analysed for a large number of transition-metal and rare-earth compounds. Calculations of the spectra have been performed at different levels of complexity, but generally within an Anderson impurity Hamiltonian. In the case of metallic systems, the situation is complicated by the presence of a continuum of low-energy electron-hole excitations across the Fermi level. These play an important role in the case of the rare earths and their intermetallics. This effect is particularly important for the valence-band spectra. 

Fig. 21. Real part of the conductivity of YbFe4St>i2- The symbols on die left axis represent dc values at different temperatures. Below T (fv 50 K), a narrow peak at zero frequency and a gap-like feature at 18 meV gradually develop. Inset Renormalized band structure calculated from die Anderson lattice Hamiltonian. % and f denote bands of free carriers and localized electrons, respectively. At low temperatures a direct gap A opens. The Fermi level, Ep is near die top of die lower band,, resulting in hole-like character and enhanced effective mass of die quasiparticles (Dordevic et al., 2001).

With increasing the hole concentration the Fermi surface of the t-J model is transformed to a rhombus centered at Q [16], This result is in agreement with the Fermi surface observed in La2-xSrxCuC>4 [19] [however, to reproduce the experimental Fermi surface terms describing the hole transfer to more distant coordination shells have to be taken into account in the kinetic term of Hamiltonian (1)]. For such x another mechanism of the dip formation in the damping comes into effect. The... 

From the above mentioned relations it is easy to see that the vacuum expectation value of the electronic Hamiltonian (3.4) is zero. The particle-hole formalism implies a redefinition of the vacuum state. Since correlation energy is defined with respect to the Hartree-Fock energy, we redefine the vacuum state as being the occupation-number vector corresponding to the converged HF determinant, the Fermi vacuum. This leads to a redefinition of creation... 

In single-reference CC the excitation operators contain only creation operators (particle or hole) with respect to the Fermi vacuum. In MRCC there is no unique choice of Fermi vacuum, but for any choice annihilation operators will appear in the excitation manifold so that the BCH-expansion of the similarity-transformed Hamiltonian will not truncate to quartic order. 

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