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Boosting the accuracy and speed of quantum Monte Carlo: Size consistency and time step

Andrea Zen, Sandro Sorella, Michael J. Gillan, Angelos Michaelides, and Dario Alfè
Phys. Rev. B 93, 241118(R) – Published 29 June 2016
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Abstract

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard for providing high-quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation relies on modifications of the Green's function to avoid singularities near the nodal surface of the trial wave function. Here we show that these modifications affect the DMC energies in a way that is not size consistent, resulting in large time-step errors. Building on the modifications of Umrigar et al. and DePasquale et al. we propose a simple Green's function modification that restores size consistency to large values of the time step, which substantially reduces time-step errors. This algorithm also yields remarkable speedups of up to two orders of magnitude in the calculation of molecule-molecule binding energies and crystal cohesive energies, thus extending the horizons of what is possible with DMC.

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  • Received 7 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.241118

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Andrea Zen1,2,3, Sandro Sorella4, Michael J. Gillan1,2,3, Angelos Michaelides1,2,3, and Dario Alfè1,2,3,5,*

  • 1London Centre for Nanotechnology, Gordon Street, London WC1H 0AH, United Kingdom
  • 2Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
  • 3Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
  • 4International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy, and INFM Democritos National Simulation Center, Trieste, Italy
  • 5Department of Earth Sciences, University College London, London WC1E 6BT, United Kingdom

  • *d.alfe@ucl.ac.uk

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Issue

Vol. 93, Iss. 24 — 15 June 2016

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