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Title: Observations on variational and projector Monte Carlo methods

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.
Authors:
 [1]
  1. Cornell Univ., Ithaca, NY (United States). Laboratory of Atomic and Solid State Physics
Publication Date:
Grant/Contract Number:
SC0006650
Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 143; Journal Issue: 16; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Research Org:
Cornell Univ., Ithaca, NY (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
1469560
Alternate Identifier(s):
OSTI ID: 1224329

Umrigar, C. J.. Observations on variational and projector Monte Carlo methods. United States: N. p., Web. doi:10.1063/1.4933112.
Umrigar, C. J.. Observations on variational and projector Monte Carlo methods. United States. doi:10.1063/1.4933112.
Umrigar, C. J.. 2015. "Observations on variational and projector Monte Carlo methods". United States. doi:10.1063/1.4933112. https://www.osti.gov/servlets/purl/1469560.
@article{osti_1469560,
title = {Observations on variational and projector Monte Carlo methods},
author = {Umrigar, C. J.},
abstractNote = {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.},
doi = {10.1063/1.4933112},
journal = {Journal of Chemical Physics},
number = 16,
volume = 143,
place = {United States},
year = {2015},
month = {10}
}

Works referenced in this record:

Ground State of the Electron Gas by a Stochastic Method
journal, August 1980