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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Variational procedure for three-body correlation

A. Osman

Published May 1, 1974• 5 citations
Publisher
DOI
10.1007/bf02787160

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•Jun 18, 2007•0 citations
Within the framework of the variational theory for strongly interacting Bose liquids, we study the optimal determination of three-body correlation factors. The Euler-Lagrange equation for the three-body correlations suggests an iterative procedure in which the three-body correlation factor is expressed as a series of diagrams containing only the pair distribution function. The long-wavelength behavior of the three-body structure function agrees formally with the prediction of quantum hydrodynamics. The simplest approximation for the optimized three-body correlation function is identical to the prediction of second-order correlated-basis-function perturbation theory. We show that this simplest approximation sums essentially the same sets of diagrams that are included in non-optimized hypernetted-chain calculations with three-body correlations. Along with the three-body correlations we include those elementary diagrams of fourth and fifth order which have a comparable topological structure. The predictions for the ground-state energy and the pair distribution function are substantially improved compared with hypernetted-chain calculations restricted to two-body correlations.
We discuss a multistep variational approach for the study of many-body correlations. The approach is developed in a boson formalism (bosons representing particle-hole excitations) and based on an iterative sequence of diagonalizations in subspaces of the full boson space. The purpose of these diagonalizations is that of searching for the best approximation of the ground state of the system. The procedure also leads us to define a set of excited states and, at the same time, of operators which generate these states as a result of their action on the ground state. We examine the cases in which these operators carry one-particle one-hole and up to two-particle two-hole excitations. We also explore the possibility of associating bosons to Tamm-Dancoff excitations and of describing the spectrum in terms of only a selected group of these. Tests within an exactly solvable three-level model are provided.
Abstract This paper describes improved trial wavefunctions for helium clusters and their use in variational QMC calculations of their binding energies, structural properties, and breathing mode vibrational excited states, for clusters of 3 to 270 atoms. The wavefunctions developed were similar to those of earlier work but included convenient analytic functions for two- and three-body correlations. All terms were of the Jastrow exponential form, based on sums of one-, two-, and three-body terms t1(ri), t2(rij), and t3(rij, rjk,rki), expressed as functions of interparticle distances. Excited-state wavefunctions for the breathing vibrational mode were obtained with the aid of procedures adapted from treatment of the quantum mechanics of liquid drop models. The interactions of helium atoms were specified as pairwise-additive with an accurate semi-empirical pair potential. Optimizations of parameters in the trial wavefunctions were carried out for individual cluster sizes with an exhaustive search procedure in a series of trial variational calculations, in which the parameters were varied to minimize the energy. A partial correlation of results was obtained by use of identical initial coordinates and random number seeds in these optimization calculations. Once the wavefunctions were optimized, longer calculations were used to determine properties of the clusters. In addition, diffusion QMC calculations were used to obtain more accurate nonvariational energies for comparisons.