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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2007

The Fermion Monte Carlo revisited

Roland Assaraf
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Michel Caffarel
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Anatole Khelif
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Résumé

In this work we present a detailed study of the Fermion Monte Carlo algorithm (FMC), a recently proposed stochastic method for calculating fermionic ground-state energies [M.H. Kalos and F. Pederiva, Phys. Rev. Lett. vol. 85, 3547 (2000)]. A proof that the FMC method is an exact method is given. In this work the stability of the method is related to the difference between the lowest (bosonic-type) eigenvalue of the FMC diffusion operator and the exact fermi energy. It is shown that within a FMC framework the lowest eigenvalue of the new diffusion operator is no longer the bosonic ground-state eigenvalue as in standard exact Diffusion Monte Carlo (DMC) schemes but a modified value which is strictly greater. Accordingly, FMC can be viewed as an exact DMC method built from a correlated diffusion process having a reduced Bose-Fermi gap. As a consequence, the FMC method is more stable than any transient method (or nodal release-type approaches). We illustrate the various ideas presented in this work with calculations performed on a very simple model having only nine states but a full sign problem. Already for this toy model it is clearly seen that FMC calculations are inherently uncontrolled.
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Dates et versions

hal-00112854 , version 1 (09-11-2006)

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Roland Assaraf, Michel Caffarel, Anatole Khelif. The Fermion Monte Carlo revisited. Journal of Physics A: Mathematical and Theoretical, 2007, 40 (6), pp.1181-1214. ⟨10.1088/1751-8113/40/6/001⟩. ⟨hal-00112854⟩
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