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Many-body wavefunctions for normal liquid $^3$He

Markus Holzmann, B. Bernu, David M. Ceperley

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We present new trial wave-functions which include 3-body correlations into the backflow coordinates and a 4-body symmetric potential. We show that our wavefunctions lower the energy enough to stabilize the ground state energies of normal liquid $^3$He in the unpolarized state at all pressures in agreement with experiment; however, quantitative discrepancies remain. Further, we include strong spin coupling into the Fermi liquid by adapting pairing wave functions. We demonstrate a new, numerically stable method to evaluate pairing functions which is also useful for Path Integrals calculations at low, but non-zero temperatures.

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Many-body wavefunctions for normal liquid 3^33He
We present new trial wave-functions which include 3-body correlations into the backflow coordinates and a 4-body symmetric potential. We show that our wavefunctions lower the energy enough to stabilize the ground state energies of normal liquid 3^33He in the unpolarized state at all pressures in agreement with experiment; however, quantitative discrepancies remain. Further, we include strong spin coupling into the Fermi liquid by adapting pairing wave functions. We demonstrate a new, numerically stable method to evaluate pairing functions which is also useful for Path Integrals calculations at low, but non-zero temperatures.
We present new trial wave functions which include three-body correlations into the backflow coordinates and a four-body symmetric potential. We show that our wave functions lower the energy enough to stabilize the ground state energies of normal liquid 3He^{3}\mathrm{He}3He in the unpolarized state at all pressures in agreement with experiment; however, quantitative discrepancies remain. Further, we include strong spin coupling into the Fermi liquid by adapting pairing wave functions. We demonstrate a new, numerically stable method to evaluate pairing functions which is also useful for path integrals calculations at low, but nonzero temperatures.
We show how a ground-state trial wave function of a Fermi liquid can be systematically improved by introducing a sequence of renormalized coordinates through an iterative backflow transformation. We apply this scheme to calculate the ground-state energy of liquid 3He^{3}\mathrm{He}3He in two dimensions at freezing density using variational and fixed-node diffusion Monte Carlo. Compared with exact transient estimate results for systems with a small number of particles, we find that variance extrapolations provide accurate results for the true ground state together with stringent lower bounds. For larger systems these bounds can in turn be used to quantify the systematic bias of fixed-node calculations. These wave functions are size consistent and the scaling of their computational complexity with the number of particles is the same as for standard backflow wave functions.
Variational many-body wave functions for the ground state of liquid 3He^{3}\mathrm{He}3He which include triplet and backflow correlations are investigated with use of Monte Carlo integration. Our energy of - 1.9\ifmmode^\circ\else\textdegree\fi{}K removes half of the discrepancy between previous Jastrow-Slater calculations and experimental results. The first exact results for mass-three bosons are also presented. Triplet correlations in the variational wave function are equally effective in lowering the energy of both mass-three bosons and 3He^{3}\mathrm{He}3He.
The ground states of drops of spin-polarized liquid 3He^{3}\mathrm{He}3He containing 56, 84, and 120 atoms are calculated with the variational Monte Carlo method using wave functions containing pair, triplet, and backflow correlations. The calculated energies of these drops are higher by \ensuremath{\sim}0.2 K per atom than those of drops of unpolarized liquid 3He^{3}\mathrm{He}3He. The results also indicate that the equilibrium density of liquid $^{3}\mathrm{He}_{\mathrm{\ensuremath{\uparrow}}}$ is larger than that of unpolarized 3He^{3}\mathrm{He}3He by \ensuremath{\sim}5%, and that the thickness of its surface is smaller.
A new class of variational wave functions describing many-body systems with spin-dependent correlations is used to study solid 3 He. The idea of spin coherent states is used to construct a variational coherent-state wave function for solid 3 He as an antisymmetrized Jastrow-Nosanow wave function that also contains spin-dependent correlations. We investigate this wave function by a variational Monte Carlo method. The addition of triplet (three-body) correlations produces a ground-state energy per particle that is a considerable improvement upon other variational results, but still appreciable discrepancies with the experiment remain. We speculate that such discrepancies point to a non-negligible effect of more-than-three-body correlations for both liquid and solid 3 He.
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