Momentum distribution of liquid helium

TL;DR

This study uses advanced Monte Carlo simulations to analyze the momentum distribution and condensate fraction of liquid helium isotopes at low temperature, revealing insights into long-range correlations and Fermi surface behavior.

Contribution

The paper introduces optimized trial functions for DMC simulations and provides new insights into the momentum distribution and condensate fraction of liquid helium isotopes.

Findings

Condensate fraction smaller than previous estimates.

Momentum distribution compatible with long-range correlations.

Approximate factorization of the one-body density matrix for $^3$He.

Abstract

We have obtained the one--body density matrix and the momentum distribution $n(p)$ of liquid $^4$He at $T=3D0^o$K from Diffusion Monte Carlo (DMC) simulations, using trial functions optimized via the Euler Monte Carlo (EMC) method. We find a condensate fraction smaller than in previous calculations. Though we do not explicitly include long--range correlations in our calculations, we get a momentum distribution at long wavelength which is compatible with the presence of long--range correlations in the exact wave function. We have also studied $^3$He, using fixed--node DMC, with nodes and trial functions provided by the EMC. In particular, we analyze the momentum distribution $n(p)$ with respect to the discontinuity $Z$ as well as the singular behavior, at the Fermi surface. We also show that an approximate factorization of the one-body density matrix $\rho(r)\simeq \rho_0(r)\rho_B(r)$ holds, with $\rho_0(r)$ and $\rho_B(r)$ respectively the density matrix of the ideal Fermi gas and the density matrix of a Bose $^3$He.