Mirror potentials and the fermion problem

J. Carlson and M. H. Kalos
Phys. Rev. C 32, 1735 – Published 1 November 1985
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Abstract

The exact treatment of fermion systems by Monte Carlo methods has proved to be difficult. We present a new method based on the concept of a ‘‘mirror potential,’’ which is a many-body potential that forces the Monte Carlo iteration to have a stable antisymmetric component. The potential may be determined from the wave function and, within the framework of Green’s function Monte Carlo, from the random walk whose density converges to the wave function. In certain limits, the method reduces to the fixed node approximation and to transient estimation, so that it subsumes both of them. As a further consequence it offers an approximation analogous to fixed node for treating systems with noncentral forces. The method may prove to be a general one for treating random walkers with nonpositive or complex weights. In support of that we exhibit a successful calculation of a one-dimensional excited state. In this paper we explore the alternative in which the mirror potential is obtained from trial wave functions. This yields an approximation scheme that proves to be accurate in the experiments described here. We present results for a model problem in which four neutrons interact by a spin-independent potential, and compare the results with those of the fixed node method, and the method of transient estimation.

  • Received 30 May 1985

DOI:https://doi.org/10.1103/PhysRevC.32.1735

©1985 American Physical Society

Authors & Affiliations

J. Carlson and M. H. Kalos

  • Courant Institute of Mathematical Sciences, New York University, New York, New York 10012

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Issue

Vol. 32, Iss. 5 — November 1985

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