Roi Baer
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The Chaim Weizmann Institute of Chemistry, and the Fritz Haber Research Center for Molecular Dynamics,
The Hebrew University of Jerusalem, Jerusalem 91904, Israel. Tel: +972-2-658-6114 Fax: +972-2-651-3742
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Straddle

למעלה

J. Chem Phys. 109, 6219 (1998)

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Shifted contour auxiliary field Monte-Carlo for electronic structure: Straddling the Fermion sign problem

Roi Baer and Martin Head-Gordon
Department of Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720

Daniel Neuhauser
Department of Chemistry and Biochemistry, University of California, Los-Angeles, CA 90095-1569

Abstract - The auxiliary field Monte-Carlo (AFMC) technique has advantages over other ab-initio quantum Monte-Carlo methods for Fermions as it does not seem to require approximations for alleviating the sign problem and is directly applicable to excited states. Yet, the method is severely limited by a numerical instability, a numerical sign problem, prohibiting application to realistic electronic structure systems. Recently, the shifted contour auxiliary field method (SC-AFMC) was proposed for overcoming this instability. Here we develop a theory for the AFMC stabilization, explaining the success of SC-AFMC.

Statistical convergence of singlet H2 correlation energy using AFMC (triangles) and SCAFMC (squares). Bond length is 1.4 au. b=2 au.
We show that the auxiliary fields can be shifted into the complex plane in a manner that considerably stabilizes the Monte-Carlo integration using the exact one electron density. Considerable stabilization can be achieved when an approximate Hartree-Fock density is used, showing that an overwhelming part of the sign problem is removed by taking proper account of the Fermion mean field density. The theory is demonstrated by application to H2.

Background- Auxiliary Field Monte Carlo (AFMC) is a Quantum Monte-Carlo method for calculating propeties of many particle systems, where the particles are interacting via a two body potential. For electronic structure, AFMC has been, until recently of limited use, because of the Fermion Sign Problem. Recently the group of D. Neuhauser from UCLA has suggested the shifted countour AFMC (SCAFMC) to alleviate the sign problem. This paper on AFMC discusses theoretically the SCAFMC and demonstrates its performance on a H2 molecule (see figure).