Quantum simulation of systems with nodal surfaces

D. F. Coker, R 0. Watts

Published Jun 18, 2007• 0 citations

Abstract

Abstract Coker and Watts reported modifications of the simple diffusion QMC algorithm to treat the problem of node location in small systems. This enabled the calculation of low-lying states for a vibrating diatomic molecule as well as electronic structures for H 2p, He 3S, and Li 1S. The general method makes use of cancellation of positive and negative walkers occupying the same volume elements of a grid in the coordinate space of the walkers, together with appropriate constraints to prevent decay to a lower-energy solution. In the case of molecular vibration, orthogonality to lower states was enforced by maintaining equal weights of positive and negative walkers in equivalent regions of coordinate space for lower states. For the case of fermion ground states for He 3S and Li 1S, equal weights of positive and negative walkers were required for all coordinate space. For the higher dimensionality of the Li case, cancellation was based on proximity of walkers of opposite signs. Results in terms of energy were accurate to about three digits and within their uncertainties overlapped accepted values for each of the systems investigated. These provided a hint of more accurate results to be obtained later for small systems.

DOI: 10.1093/oso/9780195310108.003.0041

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