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Physical review. B, Condensed matter

Alternative to Gutzwiller’s approach

Sushil Lamba, S. K. Joshi

Published Sep 15, 1995• 2 citations
Publisher

Abstract

An efficient variational procedure to calculate the ground-state properties of the particle-hole symmetric periodic Anderson model is presented. Expectation values are calculated by using an approximate scheme. It is shown that the ground-state energy calculated with the one-site approximation, which essentially is a single-site mean-field approximation, is identical to the corresponding energy obtained by the well-known Gutzwiller wave function using the Gutzwiller approximation. The two-site approximation, in which intersite correlations are explicitly included, is shown to be a better approximation than the Gutzwiller approximation.

DOI
10.1103/physrevb.52.7972

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An efficient variational procedure to calculate the ground-state properties of the particle-hole symmetric periodic Anderson model is presented. Expectation values are calculated by using an approximate scheme. It is shown that the ground-state energy calculated with the one-site approximation, which essentially is a single-site mean-field approximation, is identical to the corresponding energy obtained by the well-known Gutzwiller wave function using the Gutzwiller approximation. The two-site approximation, in which intersite correlations are explicitly included, is shown to be a better approximation than the Gutzwiller approximation.
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We propose a new variational wave function for the periodic Anderson model in the case of antiferromagnetically ordered f-electrons. Expectation values in terms of this wave function can be calculated analytically in arbitrary dimensions d. The wave function automatically produces the exact limiting behavior of the ground state energy for weak hybridization and strong f-electron interaction in the symmetric case, which the Gutzwiller wave function fails to do. Several additional improvements are discussed. Thereby one obtains a wave function that leads to extremely good ground state energies for the periodic Anderson model for arbitrary U in all dimensions d.
A new analytic approach to the evaluation of ground-state properties of Hubbard-type models in terms of the Gutzwiller variational wave function is presented. It is based on the observation that expectation values in terms of this wave function may be expressed by sums over different lattice sites. This makes the application of Wick's theorem and the resulting contractions extremely simple, since the latter involve only anticommuting numbers as in a Grassmann algebra. Expressions for the momentum distribution ${n}_{\mathrm{k}\ensuremath{\sigma}}$ and the Hubbard interaction in terms of a power series in a particular correlation parameter are derived which are valid for all dimensions. An explicit diagrammatic evaluation of the coefficients is described. In one dimension these coefficients may be determined to all orders which yields an approximation-free calculation of nk{n}_{\mathrm{k}}nk​ and ground-state energy E for arbitrary density n and interaction strength U. In the case of a half-filled band and large U, hitherto unexpected nonanalyticities are found. The results allow for the first approximation-free assessment of the properties of the Gutzwiller wave function. It is shown that the well-known Gutzwiller approximation may be derived diagrammatically, too. The approximation is seen to yield the exact results for expectation values in terms of this wave function in the limit of infinite dimensionality.
Abstract We discuss a variational ground state wave function for the symmetric periodic Anderson model with commensurate spin density order. The energy of this ansatz is evaluated in closed form. Our approach generalizes a variational treatment proposed recently by Strack and Vollhardt and results in significantly lower energy. Contrary to the Gutzwiller ansatz the wave function recovers the Schrieffer‐Wolff limit for large Coulomb repulsion. We clarify the relation of our approach to unrestricted Hartree‐Fock and present a comparison with existing quantum Monte Carlo calculations for one dimension.