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Physical review. B, Condensed matter

Variational calculations of drops of spin-polarized liquid He3

D. S. Lewart, Vijay R. Pandharipande, Steven C. Pieper

Published Jul 1, 1989• 1 citation
Publisher

Abstract

The ground states of drops of spin-polarized liquid $^{3}\mathrm{He}$ 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 $^{3}\mathrm{He}$. The results also indicate that the equilibrium density of liquid $^{3}\mathrm{He}_{\mathrm{\ensuremath{\uparrow}}}$ is larger than that of unpolarized $^{3}\mathrm{He}$ by \ensuremath{\sim}5%, and that the thickness of its surface is smaller.

DOI
10.1103/physrevb.40.712

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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 3He\ensuremath↑^{3}\mathrm{He}_{\mathrm{\ensuremath{\uparrow}}}3He\ensuremath↑​ is larger than that of unpolarized 3He^{3}\mathrm{He}3He by \ensuremath{\sim}5%, and that the thickness of its surface is smaller.
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.
Drops containing 20 to 240 atoms of Bose liquid 4He^{4}\mathrm{He}4He and Fermi liquid 3He^{3}\mathrm{He}3He are studied by variational Monte Carlo methods as simple examples of correlated inhomogeneous quantum systems. In the present work we report wave functions of natural, quasiparticle, and mean-field orbitals in these drops. The wave functions of natural orbitals are determined by diagonalizing the one-particle density matrix. The condensate fraction and wave function in the Bose-liquid drops are calculated. The quasihole states are defined in the spirit of Landau's theory, and their wave functions are calculated from the overlaps between states containing N and N-1 atoms. In Bose-liquid drops the wave function of the quasihole orbital is similar to that of the condensate; however, in Fermi-liquid drops the quasihole wave functions are different from those of natural or mean-field orbitals. We find that a simple local-density approximation provides an accurate relation between the mean-field and quasihole wave functions for both Bose- and Fermi-liquid drops. The wave functions of natural orbitals are very localized and simple methods to construct them from mean-field wave functions are also discussed. The momentum distributions of atoms in the drops are calculated and compared with those of extended liquids. The deviations of the momentum distributions from mean-field distributions are also discussed.
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.
Microscopic prediction of the ground-state phase of electron-spin-aligned bulk atomic deuterium (D\ensuremath{\downarrow}) is attempted, based on the variational Monte Carlo method. The accurate pair potential of Kolos and Wolniewicz is assumed, and three versions of D\ensuremath{\downarrow} are considered, which, respectively, involve one, two, and three equally occupied nuclear spin states. The most definitive results on the zero-temperature equations of state of these systems are obtained with optimized ground-state trial wave functions incorporating Jastrow pair correlations, triplet correlations, and momentum-dependent backflow effects. The species D${\ensuremath{\downarrow}}_{3}$ is bound already at the pure Jastrow level, while the energy expectation value of D${\ensuremath{\downarrow}}_{2}$ dips below zero upon supplementing the Jastrow description by triplets and momentum-dependent backflow. The variational energy of D${\ensuremath{\downarrow}}_{1}$ remains positive under all current refinements of the ground-state trial function. We conclude that the systems D${\ensuremath{\downarrow}}_{3}$ and D${\ensuremath{\downarrow}}_{2}$, if they could be manufactured and stabilized at relevant densities, would be Fermi liquids at sufficiently low temperature; on the other hand, it is likely that D${\ensuremath{\downarrow}}_{1}$ would remain gaseous down to absolute zero.
The ground-state properties of one-dimensional 3He^{3}\mathrm{He}3He are studied using quantum Monte Carlo methods. The equation of state is calculated in a wide range of physically relevant densities and is well interpolated by a power-series fit. The Luttinger liquid theory is found to describe the long-range properties of the correlation functions. The density dependence of the Luttinger parameter is explicitly found, and interestingly it shows a nonmonotonic behavior. Depending on the density, the static structure factor can be a smooth function of the momentum or might contain a peak of a finite or infinite height. Although no phase transitions are present in the system, we identify a number of physically different regimes, including an ideal Fermi gas, a ``Bose gas.'' a ``super-Tonks-Girardeau'' regime, and a ``quasicrystal.'' The obtained results are applicable to unpolarized, partially, or fully polarized 3He^{3}\mathrm{He}3He.
Variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions are used to study the spin-polarized three-dimensional uniform electron fluid. We report ground state VMC and DMC energies in the density range $0.5\ensuremath{\le}{r}_{\text{s}}\ensuremath{\le}20$. Finite-size errors are corrected using canonical-ensemble twist-averaged boundary conditions and extrapolation of the twist-averaged energy per particle calculated at three system sizes (N=113,259,and387)(N=113, 259, \mathrm{and} 387)(N=113,259,and387) to the thermodynamic limit of infinite system size. The DMC energies in the thermodynamic limit are used to parametrize a local spin density approximation correlation function for inhomogeneous electron systems.