Observations on variational and projector Monte Carlo methods

Umrigar, C. J.

doi:10.1063/1.4933112

Observations on variational and projector Monte Carlo methods

Journal Article · Mon Oct 26 04:00:00 EDT 2015 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4933112· OSTI ID:1469560

Umrigar, C. J. ^[1]

Cornell Univ., Ithaca, NY (United States). Laboratory of Atomic and Solid State Physics; Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853

In this work, variational Monte Carlo and various projector Monte Carlo (PMC) methods are presented in a unified manner. Similarities and differences between the methods and choices made in designing the methods are discussed. Both methods where the Monte Carlo walk is performed in a discrete space and methods where it is performed in a continuous space are considered. It is pointed out that the usual prescription for importance sampling may not be advantageous depending on the particular quantum Monte Carlo method used and the observables of interest, so alternate prescriptions are presented. The nature of the sign problem is discussed for various versions of PMC methods. A prescription for an exact PMC method in real space, i.e., a method that does not make a fixed-node or similar approximation and does not have a finite basis error, is presented. This method is likely to be practical for systems with a small number of electrons. Lastly, approximate PMC methods that are applicable to larger systems and go beyond the fixed-node approximation are also discussed.

View Accepted Manuscript (DOE)

Research Organization:: Cornell Univ., Ithaca, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0006650

OSTI ID:: 1469560

Alternate ID(s):: OSTI ID: 1224329
OSTI ID: 22493144

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 16 Vol. 143; ISSN JCPSA6; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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