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Article overview
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Critiquing Variational Theories of the Anderson-Hubbard Model: Real-Space Self-Consistent Hartree-Fock Solutions | | X. Chen
; A. Farhoodfar
; T. McIntosh
; R. J. Gooding
; P.W. Leung
; | | Date: |
28 Aug 2008 | | Abstract: | A simple and commonly employed approximate technique with which one can
examine spatially disordered systems when strong electronic correlations are
present is based on the use of real-space unrestricted self-consistent
Hartree-Fock wave functions. In such an approach the disorder is treated
exactly while the correlations are treated approximately. In this report we
critique the success of this approximation by making comparisons between such
solutions and the exact wave functions for the Anderson-Hubbard model. Due to
the sizes of the complete Hilbert spaces for these problems, the comparisons
are restricted to small one-dimensional chains, up to ten sites, and a 4x4
two-dimensional cluster, and at 1/2 filling these Hilbert spaces contain about
63,500 and 166 million states, respectively. We have completed these
calculations both at and away from 1/2 filling. This approximation is based on
a variational approach which minimizes the Hartree-Fock energy, and we have
completed comparisons of the exact and Hartree-Fock energies. However, in order
to assess the success of this approximation in reproducing ground-state
correlations we have completed comparisons of the local charge and spin
correlations, including the calculation of the overlap of the Hartree-Fock wave
functions with those of the exact solutions. We find that this approximation
reproduces the local charge densities to quite a high accuracy, but that the
local spin correlations, as represented by < S_i . S_j >, are not as well
represented. In addition to these comparisons, we discuss the properties of the
spin degrees of freedom in the HF approximation, and where in the
disorder-interaction phase diagram such physics may be important. | | Source: | arXiv, 0808.3899 | | Services: | Forum | Review | PDF | Favorites | |
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