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Physical review. B, Condensed matter

Shadow wave function for many-boson systems

L. Reatto, G. L. Masserini

Published Sep 1, 1988• 64 citations
Publisher

Abstract

Some properties of a new class of variational wave functions for boson systems are studied. This study extends the Jastrow class, and many-body correlations are implicitly introduced by a coupling of the particle coordinates to subsidiary shadow variables. We prove that the new wave function has Bose-Einstein condensation both in the liquid and in the solid phase. The maximum-overlap criterion for this wave function with the exact ground state is developed. The kind of Jastrow correlations implicitly contained in the new wave function is studied and we formulate a theory of correlations based on the reference interaction site model.

DOI
10.1103/physrevb.38.4516

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By a Monte Carlo variational calculation, it is shown that the description of the ground-state properties of a hard-sphere Bose system is improved if the Jastrow wave function contains a correlation structure at distances intermediate between the first and the second shell of neighbors. We relate these correlations to the zero-point motion of rotons. We predict that the oscillations of the structure factor S(k)S(k)S(k) and of the radial distribution function g(r)g(r)g(r) increase at finite temperatures. Such intermediate-distance correlations improve the description of the solid phase by a Jastrow wave function, but the description is still not satisfactory compared to localized wave functions. Backflow associated with rotons induces explicit three-particle correlations in the wave function, and a new form for such correlations is proposed for variational calculation for 4He^{4}\mathrm{He}4He.
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A new class of variational wave functions describing many-body systems with spin-dependent correlations is used to study solid 3 He. The idea of spin coherent states is used to construct a variational coherent-state wave function for solid 3 He as an antisymmetrized Jastrow-Nosanow wave function that also contains spin-dependent correlations. We investigate this wave function by a variational Monte Carlo method. The addition of triplet (three-body) correlations produces a ground-state energy per particle that is a considerable improvement upon other variational results, but still appreciable discrepancies with the experiment remain. We speculate that such discrepancies point to a non-negligible effect of more-than-three-body correlations for both liquid and solid 3 He.
A new variational wave function is proposed for the ground state of Bose liquids. It consists of a Jastrow function multiplied by exponentials of three-particle functions. The form of the wave function is deduced from a formal analysis carried out for the weakly interacting Bose gas characterized by a strength parameter $\ensuremath{\lambda}$. By using the wave function proposed here, the energy obtained is exact to $O({\ensuremath{\lambda}}^{4})$. Several useful and straightforward applications of the new method to liquid helium and Coulomb gases are suggested.
The problem of how to extract information on the structure of the exact ground-state wave function of a Bose fluid from the results of Green's-function Monte Carlo computations is considered. Use of the criterion of maximum overlap of the exact ground state with an extended Jastrow function leads to certain equalities for correlation functions. By using methods borrowed from theories of classical fluids various schemes are proposed that permit the determination of the "best" Jastrow function. The case of Fermi statistics is also considered.