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Molecular Physics

Variational localized-site cluster expansions

Daniel Klein, M. A. García‐Bach

Published Mar 1, 1976• 7 citations
Publisher

Abstract

The simplest variational localized-site cluster expansions for Hubbard and Pariser-Parr-Pople (PPP) models are considered and explicit matrix element formulae are developed. Numerical calculations for infinite chains and finite cycles are reported. It is found that even the simplest ansatz yields results in the atomic limit which are better than other conventional techniques. Near the band limit its accuracy decreases, as expected, but the next most simple ansatz does better.

DOI
10.1080/00268977600100611

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The Journal of Chemical Physics•Jun 15, 1976•8 citations
The simplest variational localized-site cluster expansions for Hubbard and Pariser-Parr-Pople (PPP) models are considered and explicit matrix element formulae are developed. Numerical calculations for infinite chains and finite cycles are reported. It is found that even the simplest ansatz yields results in the atomic limit which are better than other conventional techniques. Near the band limit its accuracy decreases, as expected, but the next most simple ansatz does better.
Abstract A general and systematic localized‐site cluster expansion is described. It provides simple physically appealing and computationally feasible wave function ansätze, as well as, via extension of the cluster expansion, a unique expression for general, possibly exact, wave functions. We show that a variety of matrix element evaluation techniques are available and that they are sometimes exact though relatively simple. These techniques often proceed in terms of computational time proportional to the number of different types of sites, rather than their total number. Thus it seems we have a new and viable many‐body theory, which is expected to be most accurate and most readily implementable when a physical picture with slightly perturbed localized sites is relevant.