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arXiv:cond-mat/0605513 · Physical Review B

Many-body wavefunctions for normal liquid He3

Markus Holzmann, B. Bernu, David M. Ceperley

Published Sep 26, 2006• 39 citations
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Abstract

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 $^{3}\mathrm{He}$ 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 nonzero temperatures.

DOI
10.1103/physrevb.74.104510

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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.
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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.
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.
The possible superfluidity of a system of strongly interacting fermions is investigated on the assumption that an adequate description of the system in its "normal" state is given by independent fermions in a momentum-dependent potential. On the basis of this assumption we have investigated whether a correlated wave function of the form used by Bardeen, Cooper, and Schrieffer minimizes the ground-state energy. The nonzero terms in the expectation value of the Hamiltonian contain the modified kinetic energy and the full two-body potential between the fermion pairs. An integral equation is obtained in configuration space for the correlation function between pairs. This integral equation is meaningful even for potentials with hard cores, and a nonzero solution implies the existence of a superfluid state. A variational method is devised which provides a criterion for superfluidity and a lower bound for the transition temperature into the superfluid state. We find that a repulsive hard core does not in principle forbid the existence of a superfluid state, but whereas in the absence of a hard core an attractive two-body potential always leads to a superfluid state at sufficiently low temperatures, in the presence of a repulsive core there appears to be a critical strength of attraction needed to form a superfluid state. When the variational principle is applied to liquid He3{\mathrm{He}}^{3}He3 or to nuclear matter, it is found for a wide class of trial functions that the system does not become a superfluid.