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Journal of Physics Condensed Matter

The coherent-state wave function for solid3He

Orion Ciftja, Saverio Moroni, Stefano Fantoni

Published Jan 25, 2001• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/13/5/317

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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.
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 description of the properties of liquid Helium is a challenge for any microscopic many-body theory. In this context, we study the ground state and the excitation spectrum of one 3 He impurity in liquid 4 He at T=0 with the aim of illustrating the power of the correlated basis function formalism in describing heavily correlated systems. The strong interatomic interaction and the large density require the theory to be pushed to a high degree of sophistication. A many-body correlation operator containing explicit two- and three-particle correlation functions is needed to obtain a realistic ground state wave function, whereas a perturbative expansion including up to two phonon correlated states must be enforced to study the impurity excitation energies. The theory describes accurately the experimental spectrum along all the available momentum range. As empirically shown by the experiments, a marked deviation from the quadratic Landau-Pomeranchuck behavior is found and the momentum dependent effective mass of the impurity increases of ~50% at q~1.7 Å-1 with respect to its q=0 value. Although the main emphasis is given to the correlated basis function theory, we present also comparisons with other methods, as diffusion Monte Carlo, variational Monte Carlo with shadow wave functions and time dependent correlations.
Some properties of a new class of variational wave functions for boson systems are studied. This study extends the Jastrow class, and many-body correlations are implicitly introduced by a coupling of the particle coordinates to subsidiary shadow variables. We prove that the new wave function has Bose-Einstein condensation both in the liquid and in the solid phase. The maximum-overlap criterion for this wave function with the exact ground state is developed. The kind of Jastrow correlations implicitly contained in the new wave function is studied and we formulate a theory of correlations based on the reference interaction site model.
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 theory is developed to allow the systematic calculation of the properties of quantum fluids given the microscopic two-body potential. Physical arguments are used to construct a correlation operator that approximately transforms the states of a non-interacting system into the corresponding states of the interacting-system. The theory can be regarded as a microscopic realization of Landau's assumption of a one-to-one correspondence between the non-interacting and interacting states. It is variational since the correlation operator is determined by minimizing E(p) the expectation value of the ground-state energy. We first give a survey of various other many-body theories including the simpler Jastrow variational method. Differential equations are derived to calculate the correlation operator and the related Jastrow correlation"" function. A comparison of results in several Bose systems with various methods is given. The Fermi hypernetted chain integral equations are generalized to allow the calculation of E(p) in Fermi systems, using the correlation operator wave function. The method is applied to liquid 3He and the v2-model of nuclear matter. In 3He the correlation operator gives results in much closer agreement with experiment than that with the Jastrow wave function. A new set of hypernetted chain equations are then derived to allow the calculation of the excited st;ate energies in Bose systems. The theory is then applied to the calculation of the single quasi-particle excitation spectrum of liquid 4He. The spectrum is found to be a stringent test on the form of the correlation operator, deficiencies in the correlation operator giving corresponding errors in the spectrum. Good results are obtained for the density dependence of the roton energy. A variational principle for the free energy is used to generalize the correlation operator technique to finite temperatures. Results are given for the finite temperature properties of the v8-model of nuclear matter."
We propose a variational wave function which uses coherent states to represent the spin state of particles, and describes systems with spin-dependent correlations. Spin states are parametrized by a continuous variable that looks like a classical spin vector. Correlation operators are represented as simple integrals, without commutator terms, which can be evaluated using standard or Monte Carlo techniques. Explicit calculations on liquid 3{}^{3}3He using our wave function give good agreement with standard methods. Applications to systems in condensed matter and nuclear physics are discussed.