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Many-Electron Trial Wave Functions for Inhomogeneous Solids

R. Gaudoin·M. Nekovee·W. M. C. Foulkes·R. J. Needs·G. Rajagopal
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Abstract

Quantum Monte Carlo simulations of interacting electrons in solids often use Slater-Jastrow trial wave functions with Jastrow factors containing one- and two-body terms. In uniform systems the long-range behavior of the two-body term may be deduced from the random-phase approximation (RPA) of Bohm and Pines. Here we generalize the RPA to nonuniform systems. This gives the long-range behavior of the inhomogeneous two-body correlation term and provides an accurate analytic expression for the one-body term. It also explains why Slater-Jastrow trial wave functions incorporating determinants of Hartree-Fock or density-functional orbitals are close to optimal even in the presence of an RPA Jastrow factor. After adjusting the inhomogeneous RPA Jastrow factor to incorporate the known short-range behavior, we test it using variational Monte Carlo calculations. We find that the most important aspect of the two-body term is the short-range behavior due to electron-electron scattering, although the long-range behavior described by the RPA should become more important at high densities.

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R. Gaudoin, M. Nekovee, W. M. C. Foulkes, R. J. Needs, G. Rajagopal. 2000-05-18. Many-Electron Trial Wave Functions for Inhomogeneous Solids. https://arxiv.org/abs/cond-mat/0005305

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