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Journal of the Nigerian Association of Mathematical Physics

Correlation between perturbation and variation methods in the study of strongly correlated electron systems

Robinson O. Okanigbuan, JO Idiodi

Published May 22, 2008• 0 citations
Publisher

Abstract

The ground–state wave function and energy are calculated for two electrons subject to a one-band Hubbard Hamiltonian on a one dimensional lattice containing N electronic sites, N = 2,3,4,5,6, and a 3 x 3 cluster of the square lattice, using perturbation and variational methods. The results from these two approximation methods are then compared with the result from exact calculational method. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 583-594

DOI
10.4314/jonamp.v10i1.40182

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The ground–state wave function and energy are calculated for two electrons subject to a one-band Hubbard Hamiltonian on a one dimensional lattice containing N electronic sites, N = 2,3,4,5,6, and a 3 x 3 cluster of the square lattice, using perturbation and variational methods. The results from these two approximation methods are then compared with the result from exact calculational method. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 583-594
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We study the one-band Hubbard model in a three dimensional simple cubic lattice, with periodic boundary conditions, by means of a variational analytic approach. Ground state energies and pairing correlations depend implicitly on the interaction strength (U/41). It is shown that for two electrons, the interaction is always repulsive in the ground state for any positive value of the on-site Coulomb interaction U. Implications of this result for superconductivity are also discussed. Nigerian Journal of Physics Vol. 16(2) 2004: 167-171
The ground-state wave function and energy are calculated for the one-band Hubbard Hamiltonian on a 4\ifmmode\times\else\texttimes\fi{}4 cluster of the square lattice up to first and second order of the on-site Coulomb repulsion U, respectively. Changes induced by a deviation of the number of electrons from half-filling (one electron per lattice site) are closely followed. Charge-charge and spin-spin correlation functions are directly obtained from the ground-state wave function and show the existence of antiferromagnetic correlations that extend over the whole cluster at half-filling. Correlations among sites separated by more than a lattice site diminish very rapidly as holes are introduced into the cluster. The analysis is extended to the negative-U case. Ground-state properties change qualitatively.
A new variational method is developed to calculate the ground state energy of Fermi systems with strong short-range correlations. A trial wave function of Gutzwiller's type contains additional variational parameters corresponding to configurations of pairs of nearest-neighbor sites. To evaluate the ground state energy, generalized Kikuchi's pseudo-ensemble method is used. The Hubbard model at half band-filling is investigated. The ground state energy of the paramagnetic phase is calculated for a chain, square and simple cubic lattices. It is shown that the short-range order lowers drastically the ground state energy of the Hubbard model at intermediate interaction strength. The paramagnetic phase of the Kondo-Hubbard model (S=1/2S=1/2S=1/2 and S=5/2S=5/2S=5/2) at half band-filling is investigated. The ground state energy, correlation functions and effective mass are calculated for chain, square and simple cubic lattices. A quantum phase transition was found for simple cubic lattice.