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arXiv:1607.05921 · Physical review. B./Physical review. B

Jastrow correlation factor for periodic systems

Thomas M. Whitehead, M. H. Michael, G. J. Conduit

Published Jul 28, 2016• 14 citations
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Abstract

We propose a Jastrow factor for electron-electron correlations that interpolates between the radial symmetry of the Coulomb interaction at short interparticle distance and the space-group symmetry of the simulation cell at large separation. The proposed Jastrow factor captures comparable levels of the correlation energy to current formalisms, is 40% quicker to evaluate, and offers benefits in ease of use, as we demonstrate in quantum Monte Carlo simulations.

DOI
10.1103/physrevb.94.035157

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We propose a Jastrow factor for electron-electron correlations that interpolates between the radial symmetry of the Coulomb interaction at short interparticle distance and the space-group symmetry of the simulation cell at large separation. The proposed Jastrow factor captures comparable levels of the correlation energy to current formalisms, is 40% quicker to evaluate, and offers benefits in ease of use, as we demonstrate in quantum Monte Carlo simulations.
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One of the standard approaches to calculate the ground-state properties of strongly correlated electronic systems is to use a Jastrow–Slater wavefunction as a starting point. When considering confined electrons in a two-dimensional parabolic quantum dot, one chooses the Slater determinant to be the ground-state wavefunction of confined independent electrons and then determines the form of the Jastrow correlation factor in a way that incorporates accurately the spatial correlations of the system. One way to choose a quality Jastrow correlation factor is to consider the two-body problem and search the best possible yet simple approximative solution to such a problem. To achieve this goal, we consider the two-body problem of confined electrons interacting with a Coulomb repulsive potential in zero magnetic field and focus on their relative motion. Based on straightforward theoretical considerations, we suggest a simple two-body Jastrow correlation factor that optimizes very well the overall trial energy. We test the quality of the proposed Jastrow correlation factor by comparing the results to exact numerical diagonalization solutions.
We study a system of interacting electrons on a one-dimensional quantum ring using exact diagonalization and the variational quantum Monte Carlo method. We examine the accuracy of the Slater-Jastrow -type many-body wave function and compare energies and pair distribution functions obtained from the two approaches. Our results show that this wave function captures most correlation effects. We then study the smooth transition to a regime where the electrons localize in the rotating frame, which for the ultrathin quantum ring system happens at quite high electron density.
Based on the random-phase approximation and the transcorrelated (TC) method, we optimize the Jastrow factor together with one-electron orbitals in the Slater determinant in the correlated wave function with a new scheme for periodic systems. The TC method is one of the promising wave function theories for first-principles electronic structure calculation, where the many-body wave function is approximated as a product of a Slater determinant and a Jastrow factor, and the Hamiltonian is similarity-transformed by the Jastrow factor. Using this similarity-transformed Hamiltonian, we can optimize the one-electron orbitals without evaluating 3N-dimensional integrations for the N-electron system. In contrast, optimization of the Jastrow factor within the framework of the TC method is computationally much more expensive and has not been performed for solid-state calculations before. In this study, we also benefit from the similarity-transformation in optimizing the Jastrow factor. Our optimization scheme is tested in applications to some solids from narrow-gap semiconductors to wide-gap insulators, and it is verified that the band gap of a wide-gap insulator and the lattice constants of some solids are improved by this optimization with reasonable computational cost.