Monte Carlo simulation of a many-fermion study

TLDR

The Metropolis Monte Carlo method samples the square of an antisymmetric wave function composed of a Jastrow factor and multiple Slater determinants, enabling variational energy calculations for $^3$He and neutron matter models. The first‑order Wu‑Feenberg expansion consistently underestimates energies, sometimes severely, and the ground‑state Yukawa matter phase diagram reveals a class of potentials that avoid crystallization at any density.

Abstract

The Metropolis Monte Carlo method is used to sample the square of an antisymmetric wave function composed of a product of a Jastrow wave function and a number of Slater determinants. We calculate variational energies for $^{3}\mathrm{He}$ and several models of neutron matter. The first-order Wu-Feenberg expansion is shown always to underestimate the energy, sometimes seriously. The phase diagram for ground-state Yukawa matter is determined. There is a class of Yukawa potentials which do not lead to a crystal phase at any density.