Systematic reduction of sign errors in many-body calculations of atoms and molecules

Abstract

The self-healing diffusion Monte Carlo algorithm (SHDMC) [Phys. Rev. B {\bf 79}, 195117 (2009), {\it ibid.} {\bf 80}, 125110 (2009)] is shown to be an accurate and robust method for calculating the ground state of atoms and molecules. By direct comparison with accurate configuration interaction results for the oxygen atom we show that SHDMC converges systematically towards the ground-state wave function. We present results for the challenging N${}_2$ molecule, where the binding energies obtained via both energy minimization and SHDMC are near chemical accuracy (1 kcal/mol). Moreover, we demonstrate that SHDMC is robust enough to find the nodal surface for systems at least as large as C${}_{20}$ starting from random coefficients. SHDMC is a linear-scaling method, in the degrees of freedom of the nodes, that systematically reduces the fermion sign problem.

Final version accepted in Physical Review Letters. The review history (referees' comments and our replies) is included in the source.

References in corpus (7)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Continuum variational and diffusion quantum Monte Carlo calculations
• Beyond the locality approximation in the standard diffusion Monte Carlo method
• Energy and variance optimization of many body wave functions
• Self-healing diffusion quantum Monte Carlo algorithms: methods for direct reduction of the fermion sign error in electronic structure calculations
• A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations
• Systematic reduction of sign errors in many-body problems: generalization of self-healing diffusion Monte Carlo to excited states

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