Critiquing variational theories of the Anderson–Hubbard model: real-space self-consistent Hartree–Fock solutions

摘要: 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 wavefunctions. In such an approach disorder treated exactly while approximately. this paper we critique success approximation by making comparisons between solutions exact wavefunctions for Anderson–Hubbard model. Due to sizes complete Hilbert spaces these problems, restricted small one-dimensional chains, up ten sites, a 4 × two-dimensional cluster, at 1/2-filling contain about 63 500 166 million states, respectively. We have completed calculations both away from 1/2-filling. This variational minimizes energy, energies. However, in order assess reproducing ground-state local charge spin correlations, including calculation overlap those solutions. find that reproduces densities quite high accuracy, but as represented , not well represented. addition comparisons, discuss properties degrees freedom HF approximation, where disorder–interaction phase diagram physics may be important.