Function Monte Carlo Calculations Research Articles

Static dielectric response of the electron gas.

We determine the static dielectric function of the electron gas at selected densities by using variational and fixed-node diffusion quantum Monte Carlo to find the response to a sinusoidal electric field. The dielectric function is then calculated by relating the induced charge density to the change in ground-state energy as a function of the amplitude of the applied field. A released-node Green's-function Monte Carlo calculation shows that the diffusion results are exact within the determined error bars, apart from the size dependence correction for extrapolation to the thermodynamic limit. The dielectric response is consistent at long wavelengths with the compressibility sum rule derived from a fit to Ceperley and Alder's Green's-function Monte Carlo results, but exhibits dfferences from accepted dielectric models at intermediate wave vectors.

Trial shadow wave function for the ground state of 4He.

A trial shadow wave function is introduced to describe the ground state of $^{4}\mathrm{He}$ in the solid and liquid phases. We have used Monte Carlo integration to optimize the parameters of this function, and have carried out a thorough analysis of the shadow description of the system. This shows improved pair correlations, an improved condensate fraction, substantially reduced variational energies, and a good equation of state. We have explored the melting and freezing transition, and find the transition densities to be in good agreement with the exact results of Green's function Monte Carlo (GFMC) calculations. We introduce a second shadow wave function in which a basis set expansion is used to optimize the two-particle correlations. This shadow wave function yields pair-correlation functions in excellent agreement with GFMC, as well as a substantial reduction in the variational energies at all densities.

Monte-Carlo calculation of bound-state properties

We elaborate on the role of the Green's function Monte-Carlo method in connection with quantum few-body systems and their computational treatment algorithms for calculation of bound-state properties are presented. We report results obtained from Green's function Monte-Carlo calculations both of ground-state properties of the mesic moleculesdtμ,ddμ, andpdμ as well as of excited states of the three-dimensional anharmonic oscillator and thedtμ molecule.

He2Cl2 and He3Cl2 van der Waals clusters: A quantum Monte Carlo study

The results of the first variational and Green’s function Monte Carlo calculations of the vibrational ground states of He2Cl2 and He3Cl2 van der Waals (vdW) clusters are presented in this paper. The quantum dynamics of all internal degrees of freedom are treated exactly. The ground state wave function of He2Cl2 is characterized by means of the probability distribution functions of the intermolecular degrees of freedom, which reveal an exceptionally fluxional vdW complex. A simple model for the ground state of HenCl2 vdW clusters was developed. The zero-point energies of He2Cl2 and He3Cl2 predicted by this model are in remarkable agreement (to within 0.6%) with the accurate results.

Monte Carlo calculation of interaction energies for van der Waals complexes

The electronic structure Schrodinger equation is solved approximately to obtain the interaction energies for the van der Waals complexes of spin-polarized H2 and H3 and the closed shell systems of He2 and He3. Both two- and three-body components of the interaction energies are reported. The interaction energies are obtained through variational and Green's function Monte Carlo calculations using optimized wavefunctions that properly correlate the electrons.

Density dependence of the condensate fraction in superfluid 4He

New g(r) values for liquid 4He at several fixed densities are analyzed using the method of Hyland et. al. to obtain values of the condensate fraction, n o. The values of n o (π, T≅ 1K) show a decrease of about 50% between the lowest and highest densities, consistent with the decreases predicted by various theoretical calculations. They also show evidence for a curvature in the n o vs π relationship similar to that predicted by the Green Function Monte Carlo calculation of Whitlock and Panoff based on the HFDHE2 potential of Aziz et. al. By removing several doubts raised by other authors, the present study gives renewed support to the method of Hyland et al.

Quantum Monte Carlo study of polyexcitons in semiconductors.

A variational Monte Carlo method was used to calculate the binding energies and ground-state wave functions of two-, three-, and four-exciton complexes in indirect-band-gap semiconductors within the spherical-effective-mass approximation. The results for two-exciton complexes (biexcitons) have been compared with those of Green's-function Monte Carlo calculations which produce exact ground-state energies within statistical error; the variational results recover about 90% of the binding energy of these systems. For three- and four-exciton complexes in Si, we predict that the binding energy with respect to the smaller complex with one less exciton is about 2.2 meV, in fair agreement with the experimental value of 2.5 meV.

Wave functions of helium clusters

The ground and several l=0 breathing mode vibrational excited state wave functions of HeN clusters are determined for N=3–5, 20, 70, and 240, using the variational Monte Carlo method. These wave functions incorporate one-, two-, and three-particle correlation effects and give binding energies, density profiles, and vibrational excitation energies accurately. The larger clusters have liquid-like structure, characterized by a pair distribution function showing approximately two coordination shells. The smallest clusters (N=3, 4) have extensively delocalized structures, which on average are equilateral triangular and tetrahedral, respectively. The N=5 cluster has a totally symmetric average structure, which can only be described in terms of a quantum liquid. No molecular structure, whether rigid or floppy can be assigned in this case. The relative importance of various correlation effects in clusters of different sizes is analyzed and discussed. These wave functions are completely analytical and are convenient as importance functions in diffusion and Green’s function Monte Carlo calculations.

Deep-inelastic neutron scattering from liquid 4He.

Deep-inelastic neutron scattering measurements on liquid $^{4}\mathrm{He}$ have been carried out for temperatures from 0.35 to 4.2 K at a density of 0.147 g/${\mathrm{cm}}^{3}$. These measurements have a relative resolution comparable to previous reactor measurements, but at a momentum transfer of 23 A${\mathrm{\r{}}}^{\mathrm{\ensuremath{-}}1}$. This momentum transfer is sufficiently high that the differences between the observed scattering and that predicted by the impulse approximation are small and are well described by a recent theoretical treatment allowing direct information on the single-particle momentum distribution to be obtained from the scattering measurements. The scattering in the normal liquid phase is broad and featureless with a nearly Gaussian shape. The scattering in the superfluid phase is distinctly non-Gaussian with extra intensity at the peak center consistent with the presence of a Bose condensate. However, no distinct peak due to the Bose condensate is observed even when the effects of instrumental broadening are included. When deviations from the impulse approximation are taken into account using a recent theory, the experimental results at 0.35 K are in excellent agreement with ab initio ground-state variational and Green's-function Monte Carlo calculations in the superfluid at T=0 K. The results at higher temperatures are in excellent agreement with recent path-integral Monte Carlo calculations in both the normal and superfluid phases. Fits of model functions to the scattering are also presented. The average kinetic energy per atom has been determined and is in good agreement with theoretical predictions and with previous experimental results.

Green's function Monte Carlo calculations of light nuclei

Recently, Green's Function Monte Carlo methods have been developed which enable one to perform exact calculations for the ground states of three and four body nuclei. These methods allow the alpha particle to be used as a testing ground for a variety of two- and three-nucleon interaction models, both in terms of their ground state energies and a variety of other ground state expectation values. We present a brief review of GFMC methods as applied to light nuclei, including recent improvements of the algorithm and a discussion of the prospects for the inclusion of momentum-dependent terms. We then discuss results for the ground state energy, one- and two-body density distributions, D-state probability, coulomb sum rule, and momentum distributions. The GFMC results are compared to experimental results and to variational Monte Carlo calculations.

The dissociation energy of He 2+

Ab initio potential energy curves for He 2 + are computed using full CI wavefunctions in conjunction with large Gaussian and Slater basis sets. The computed curves yield rotational-vibrational transitions with errors of less than 1 cm −1. They also yield quasibound levels with energies and lifetimes in reasonable agreement with translational spectroscopy measurements. The best D e is estimated to be 2.470 eV. Green's function Monte Carlo calculations yield a very similar value, 2.466 ± 0.005.

Ground state of the two-dimensional electron gas.

Variational and fixed-node Green's-function Monte Carlo calculations have been performed to find the ground-state properties of the two-dimensional electron gas in the density range 1\ensuremath{\le}${r}_{s}$\ensuremath{\le}100. Our calculations predict a Wigner crystallization at the density ${r}_{s}$\ensuremath{\simeq}37\ifmmode\pm\else\textpm\fi{}5. The electron system is found to be in the normal- (paramagnetic) fluid state below the transition density, but the fully polarized state is very close in energy. We have tabulated the values of pair distribution function g(r), the static structure factor S(k), and the momentum distribution n(k) at several densities of interest both in the normal and the polarized phases. An estimate of the spin susceptibility \ensuremath{\chi} is also given.

Model Hamiltonians for atomic and molecular systems

A model Hamiltonian, designed to allow larger systems to be treated with the Green’s function Monte Carlo method, is introduced for atomic and molecular systems. The model reduces the statistical variance associated with Green’s function Monte Carlo calculations by reducing potential energy fluctuations in the core regions. By performing calculations of Li, LiH, and Li2 we show that this method can be used to obtain energy differences with much less computer time than required for the complete interaction. Increases in efficiency for larger systems will be even greater.

Superconductivity in the dilute electron gas.

We determine the effective interaction of quasiparticles on the Fermi surface for the electron gas in a rigid positive background. The quasiparticle scattering amplitude is calculated from the two coupled Bethe-Salpeter equations for the two-particle vertex functions in the particle-hole (p-h) channels for densities from r/sub s/ = 1 to r/sub s/ = 37. The density and spin-density mean fields are fitted to the compressibility and spin susceptibility of Green's-function Monte Carlo calculations and the local-field factors G(q) of microscopic models. We find p-wave superconductivity for 1035.

Accurate momentum distributions from computations on 3He and 4He

The momentum distribution and condensate fraction of liquid and solid 4He determined from Green's function Monte Carlo calculations using the HFDHE2 pair potential are described. The one-body density matrix and the momentum distribution for liquid 3He derived from variational and fixed-node Green's function Monte Carlo calculations are also reported.

Green's function Monte Carlo study of light nuclei.

The first Green's function Monte Carlo calculations of A=3 and 4 nuclei with spin-dependent interactions are reported. Green's function Monte Carlo methods for calculating the properties of coupled channel quantum systems are described in detail, including both exact and approximate schemes. Results are presented for A=3 and 4 nuclei with a V6 interaction. For the triton, the Green's function Monte Carlo calculations are compared with Faddeev and variational methods. Green's function Monte Carlo calculations of the alpha particle provide the first test of variational methods for systems with spin-dependent interactions. For this interaction, variational methods underestimate the binding energy of the alpha particle by \ensuremath{\approxeq}2 MeV. Other ground state properties of light nuclei have also been determined. Implications of these results for more realistic interactions are discussed, along with the possibility of future extensions of Green's function Monte Carlo methods to treat momentum dependent and three nucleon interactions.

Representation of the vacuum wave function of the U(1) lattice gauge theory.

A representation of the ground-state wave function of the U(1) lattice gauge theory, which was used in variational and Green's-function Monte Carlo calculations, is considered. It is proven that the representation is valid. An important symmetry of the representation is discussed. The harmonic limit of the U(1) lattice gauge theory is derived in this representation.

Condensate fraction and momentum distribution in the ground state of liquid 4He.

Calculations of the condensate fraction and momentum distribution of liquid $^{4}\mathrm{He}$ are carried out using variational ground-state wave functions containing two-body (Jastrow) and three-body correlations. These wave functions give a satisfactory description of the equation of state of the liquid at T=0. The calculations are performed within the scheme of hypernetted-chain equations, using the scaling approximation for evaluating the contributions of the elementary diagrams. Results are reported at densities \ensuremath{\rho}=0.365${\ensuremath{\sigma}}^{\mathrm{\ensuremath{-}}3}$, 0.401${\ensuremath{\sigma}}^{\mathrm{\ensuremath{-}}3}$, and 0.438${\ensuremath{\sigma}}^{\mathrm{\ensuremath{-}}3}$, and compared with momentum distributions obtained from experimental data and Green's-function Monte Carlo calculations.

Binding energy of positively charged acceptors in germanium - a Green's function Monte Carlo calculation

Recent spectroscopic measurements in Ge reveal positively charged acceptors consisting of an extra hole bound to a double or triple acceptor. Using the effective-mass approximation and a pseudo-atom model which permits up to four holes in the 1 s ground state, we calculate the binding energies of these positively charged acceptors by the Green's function Monte Carlo method. For double acceptors the results of the pseudo-atom model compare favorably with experiments, whereas for triple acceptors the differences are significant.

Green's-function Monte Carlo calculations on the SU(2) and U(1) lattice gauge theories

An application of the Green's-function Monte Carlo method to the Hamiltonian formulation of the SU(2) and U(1) lattice gauge theories is described. The Green's function is that of a diffusion process in the gauge group space. A small-step approximation of the diffusion distribution is used in actual calculations. Also, a variance reduction technique is implemented, importance sampling with a disordered trial wave function optimized by the variational principle. The results of computations are reported for a 3\ifmmode\times\else\texttimes\fi{}3\ifmmode\times\else\texttimes\fi{}3 spatial lattice. The quantities computed are the ground-state energy and the expectation value of the magnetic energy, as a function of the gauge coupling constant. The results are compared to variational estimates and to weak-coupling perturbation theory.