Ground-state wave function interactions

Since this Hamilton operator does not contain any electron-electron interactions it indeed describes a non-interacting system. Accordingly, its ground state wave function is represented by a Slater determinant (switching to 0S and (p rather than Osd and % for the determinant and the spin orbitals, respectively, in order to underline that these new quantities are not related to the HF model)... 

Analysis of the valence-band spectrum of NiO helped to understand the electronic structure of transition-metal compounds. It is to be noted that th.e crystal-field theory cannot explain the features over the entire valence-band region of NiO. It therefore becomes necessary to explicitly take into account the ligand(02p)-metal (Ni3d) hybridization and the intra-atomic Coulomb interaction, 11, in order to satisfactorily explain the spectral features. This has been done by approximating bulk NiO by a cluster (NiOg) ". The ground-state wave function Tg of this cluster is given by,... 

In the high-spin ferrous ion, spin-orbit interactions mix the ground state wave functions with the excited states. If the ground state is assumed to have dZ2 symmetry, then the following expressions apply for an ion in a crystal field with both rhombic and axial distortions (Edwards et al. (70). 

In this paper we present a set of ID and 2D spin-1/2 models with competing F and AF interactions for which the singlet ground-state wave function can be found exactly. This function has a special form expressed in terms of auxiliary Bose operators. This form of the wave function is similar to the MP one but with infinite matrices. For special values of model parameters it can be reduced to the standard MP form. 

For other special cases one can also construct Hamiltonians for which 4 o is a non-degenerate singlet ground-state wave function. But in these cases one have to introduce more distant interactions. 

One of these models is the spin- ladder with competing interactions of the ferro- and antiferromagnetic types at the F-AF transition line. The exact singlet ground-state wave function on this line is found in the special form expressed in terms of auxiliary Bose-operators. The spin correlators in the singlet state show double-spiral ordering with the period of spirals equal to the system size. 

The third and final approach to the electron correlation problem included briefly here is density functional theory (DFT), a review of which has been given by Kohn in his Nobel lecture [38], The Hohcnberg Kolin theorem [39] states that there is a one-to-one mapping between the potential V(r) in which the electrons in a molecule move, the associated electron density p(r), and the ground state wave function lP0. A consequence of this is that given the density p(r), the potential and wave function lf 0 are functionals of that density. An additional theorem provided by Kohn and Sham [40] states that it is possible to construct an auxiliary reference system of non-interacting... 

Here, attention will be drawn to the important work of Rosina [79] and to the subsequent discussion of his study by Mazziotti [80], As summarized in Ref. [80], Rosina showed that the ground-state 2 DM for a quantum system completely determines the exact N-electron ground-state wave function without any specific knowledge of the exact Hamiltonian except that it has no more than two-particle interactions. Mazziotti [80] points out that a consequence of this theorem is that any ground-state electronic 2 DM precisely determines within the ensemble N-representable space a unique series of higher p-DMs where 2 < p < N. He asserts that these results provide important justification for the functional description of the higher DMs in terms of the 2 DM. 

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