Fermion Monte Carlo for continuum systems

Abstract

We have been studying methods for the Monte Carlo treatment of many-fermion systems in continuous space. We use generalizations of diffusion Monte Carlo that involve ensembles of correlated pairs of random walkers that carry opposite signs. We have been able to exhibit stable long-term behavior of the random walks: the new method suppresses the usual decay of the signal-to-noise ratio of the integrals that appear in a quotient that estimates the energy. One way of checking this result is to calculate a bosonic system with the same Hamiltonian and to estimate separately the boson–fermion energy difference. Specifically, we performed a “fixed-node” calculation of 14 3He atoms, and then a “transient estimation” removing the fixed-node constraint. The rate of decay in imaginary time of the energy denominator gives a fairly accurate measure of the boson–fermion energy difference, in good agreement with the exact energy difference. This suggests a simple method of estimating fermion energies, viz., to use directly the bosonic energy and the energy difference measured in a transient calculation.