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Physical Review Letters

Comment on "Monte Carlo Evaluation of Functional Integrals Using Coherent-State Slater Determinants"

T. Troudet, S. E. Koonin

Published Sep 19, 1983• 2 citations
Publisher

Abstract

In a recent letter [1], Avishai and Richert proposed a Monte Carlo evaluation of many-fermion functional integrals using real coherent-state Slater determinants.
DOI
10.1103/physrevlett.51.1103

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Fermion quantum Monte Carlo (QMC) methods that work in a general basis space may be more effective for some problems than the traditional diffusion QMC method. Projection of the ground state energy is achieved by random walks in the space of Slater determinants whose one‐particle orbitals are expressed in terms of the chosen basis set. A complication is that the determinants will in general acquire complex phases. This a consequence of ground state Monte Carlo projection using the Hubbard‐Stratonovich transformation of the two‐body interaction. To control the resulting “sign” decay, we describe a method we have recently introduced for the propagation of phaseless determinants. The approximation relies on importance sampling with a trial wave function. The approximation has features in common with diffusion MC fixed node and lattice‐model constrained path methods. Using a planewave basis and non‐local pseudopotentials, we apply the method to Si atom, dimer, and 2, 16, 54 atom (216 electrons) bulk supercells. Single Slater determinant wave functions from density functional theory calculations were used as |ΨT〉 with no additional optimization. The calculated binding energy of Si2 and cohesive energy of bulk Si are in excellent agreement with experiments and are comparable to the best existing theoretical results.