Momentum distribution of liquid helium

Abstract

We have obtained the one--body density matrix and the momentum distribution $n(p)$ of liquid ${}^4$He at $T=3D{0}^o$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.

10 pages, REVTeX, 12 figures

References in corpus (1)

• Unbiased estimators in Quantum Monte Carlo methods: application to liquid ${}^4$He

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