Isotopic shift of helium melting pressure: Path integral Monte Carlo study

The Solid Phase of 4He: A Monte Carlo Simulation Study

The thermodynamics of solid (hcp) 4He is studied theoretically by means of unbiased Monte Carlo simulations at finite temperature, in a wide range of density. This study complements and extends previous theoretical work, mainly by obtaining results at significantly lower temperatures (down to 60 mK) and for systems of greater size, by including in full the effect of quantum statistics, and by comparing estimates yielded by different pair potentials. All the main thermodynamic properties of the crystal, e.g., the kinetic energy per atom, are predicted to be essentially independent of temperature below ∼ 1 K. Quantum-mechanical exchanges are virtually non-existent in this system, even at the lowest temperature considered. However, effects of quantum statistics are detectable in the momentum distribution. Comparison with available measurements shows general agreement within the experimental uncertainties.

Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres

Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths , densities ). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson-Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (. This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems).

Path-integral simulation of solids

The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practical techniques for the simulation of solids. Monte Carlo and molecular dynamics methods for distinguishable quantum particles are presented, with particular attention to the isothermal-isobaric ensemble. Applications of these computational techniques to different types of solids are reviewed, including noble-gas solids (helium and heavier elements), group-IV materials (diamond and elemental semiconductors), and molecular solids (with emphasis on hydrogen and ice). Structural, vibrational, and thermodynamic properties of these materials are discussed. Applications also include point defects in solids (structure and diffusion), as well as nuclear quantum effects in solid surfaces and adsorbates. Different phenomena are discussed, as solid-to-solid and orientational phase transitions, rates of quantum processes, classical-to-quantum crossover, and various finite-temperature anharmonic effects (thermal expansion, isotopic effects, electron-phonon interactions). Nuclear quantum effects are most remarkable in the presence of light atoms, so that especial emphasis is laid on solids containing hydrogen as a constituent element or as an impurity.

Computational study of the structures of gaseous helium-3 at low temperature

A computational study of gaseous helium-3 at T=5.23 K, for number densities rho N<0.0021 A(-3), analyzing the different pair and triplet structures in both the r and the k spaces, is presented. Structures in r space (i.e., instantaneous, total continuous linear response, and centroids) are determined via path-integral Monte Carlo simulations in the canonical ensemble by utilizing the Aziz-Slaman and the SAPT2 interatomic potentials. Additional results obtained with the application of two closures for triplets in r space, the Kirkwood superposition approximation and the Jackson-Feenberg convolution, are also reported. Besides, an analysis of the nonsuitability of quantum hard spheres for describing this system is included. The pair structures in k space are fixed via Ornstein-Zernike schemes appropriate for dealing with quantum diffraction effects in fluids. The effect on the quality of the computed isothermal compressibilities brought about by increasing the sample size in the simulations and by the subsequent application of a grand ensemble correction to the asymptotic behavior of the canonical pair radial correlation functions is also investigated. Furthermore, it is demonstrated analytically that the methods of classical statistical mechanics for dealing with the higher-order direct correlation functions remain fully valid for studying the higher-order correlations of path-integral centroids. By taking advantage of this result, the triplet structure factors for the centroid (also for the instantaneous) correlations are computed by following a number of distinct closures and methods that involve triplet direct correlation functions. The latter computations are intended to explore an alternative scheme to the very expensive fixing of triplet structure factors through direct path integral simulations, an alternative which is expected to yield the main features of these triplet quantities for this gas. Comparison with experiment is made wherever possible, and the results presented allow one to explain the substantial structural features existing in gaseous helium-3.

Computational study of the melting-freezing transition in the quantum hard-sphere system for intermediate densities. I. Thermodynamic results

The points where the fluid-solid (face-centered-cubic) transition takes place in the quantum hard-sphere system, for reduced densities 0.85>rhoN*>0.5 (reduced de Broglie wavelengths lambdaB*<or=0.8), have been determined via calculations of Helmholtz free energies. A number of complementary methods have been utilized, namely, path-integral Monte Carlo simulations for fixing the basic thermodynamic and structural quantities, Ornstein-Zernike computations of the fluid isothermal compressibilities using the centroid correlations, and applications of the Einstein crystal technique. Attention is paid to the evaluation of the statistical uncertainties in the isothermal compressibilities and also to the quantum implementation of the Einstein crystal technique by including explicitly the constraint of fixed center of mass. The equation of state along the fluid lambdaB* branches studied has been determined with two methods, one based on the isothermal compressibilities and the other on the usual virial estimator. Along the solid lambdaB* branches the equation of state has been fixed with the virial estimator. The results indicate that the phase transition investigated is governed by entropic effects and that the fluid-solid coexistence densities are arranged along a straight line rhoFCC*=rho(rhoF*), a behavior which at least holds even for lambdaB*<2, as revealed by completing the present analysis with data available in the literature.

Equation of state of solid 3He

We present results of diffusion Monte Carlo calculations for the bcc and hcp phases of solid 3He, using a recent ab initio interatomic potential, including two- and three-body terms. This potential is found to yield an equation of state for condensed 4He in excellent agreement with experiment, in a wide density range. For 3He, we find a systematic discrepancy, worth 0.7 K, between our computed equation of state and a commonly accepted experimental one. We attribute such a discrepancy to an improper choice of reference energy in the determination of the experimental equation of state.