arXiv subjects
Publications and source records attributed to D. M. Ceperley.
Using Path Integral Monte Carlo we calculate exchange frequencies in bulk hcp 4He as atoms undergo ring exchange. We fit the frequencies to a lattice model and examine whether such atoms could become a supersolid, that is have a non-classical rotational inertia. We find that the scaling with respect to the number of exchanging atoms is such that superfluid behavior will not be observed in a perfect 4He crystal.
Using Path Integral Monte Carlo, we have calculated exchange frequencies as electrons undergo ring exchanges of 2, 3 and 4 electrons in a ``clean'' 3d Wigner crystal (bcc lattice) as a function of density. We find pair exchange dominates and estimate the critical temperature for the transition to antiferromagnetic ordering to be roughly $1 \times 10^{-8}$Ry at melting. In contrast to the situation in 2d, the 3d Wigner crystal is different from the solid bcc 3He in that the pair exchange dominates because of the softer interparticle potential. We discuss implications for the magnetic phase diagram of the electron gas.
Path integral Monte Carlo (PIMC) simulations are used to calculate the momentum distribution of the homogeneous electron gas at finite temperature. This is done by calculating the off-diagonal elements of the real-space density matrix, represented in PIMC by open paths. It is demonstrated how the restricted path integral Monte Carlo methods can be extended in order to deal with open paths in fermionic systems where a sign problem is present. The computed momentum distribution shows significant deviations for strong correlation from free fermion results but agrees with predictions from variational methods.
The low temperature properties of fermionic solids are governed by spin exchanges. Near the melting transition, the spin-exchange energy increases as well as the relative contribution of large loops. In this paper, we check the convergence of the multi-spin exchange model and the validity of the Thouless theory near the melting of the Wigner crystal in two dimensions. Exchange energies are computed using Path Integral Monte Carlo for loop sizes up to 8, at $r_s=40$, 50 and 75. The data are then fitted to a geometric model. Then the exchange energies are extrapolated to larger sizes in order to evaluate their contributions to the leading term of the magnetic susceptibility and the specific heat. These results are used to check the convergence of the multi-spin exchange model.
Since its first description fifty years ago, the Metropolis Monte Carlo method has been used in a variety of different ways for the simulation of continuum quantum many-body systems. This paper will consider some of the generalizations of the Metropolis algorithm employed in quantum Monte Carlo: Variational Monte Carlo, dynamical methods for projector monte carlo ({\it i.e.} diffusion Monte Carlo with rejection), multilevel sampling in path integral Monte Carlo, the sampling of permutations, cluster methods for lattice models, the penalty method for coupled electron-ionic systems and the Bayesian analysis of imaginary time correlation functions.
We justify and evaluate backflow-threebody wavefunctions for a two component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use and the analytical form of the backflow function from different points of view. The resulting wavefunctions are used in Variational and Diffusion Monte Carlo calculations of the electron gas and of solid and liquid metallic hydrogen. For the electron gas, the purely analytic backflow and three-body form gives lower energies than those of previous calculations. For bcc hydrogen, analytical and optimized backflow-threebody wavefunctions lead to energies nearly as low as those from using LDA orbitals in the trial wavefunction. However, compared to wavefunctions constructed from density functional solutions, backflow wavefunctions have the advantage of only few parameters to estimate, the ability to include easily and accurately electron-electron correlations, and that they can be directly generalized from the crystal to a disordered liquid of protons.
Path Integral Monte Carlo calculations of the superfluid density throughout ^4He droplets doped with linear impurities (HCN)_n are presented. After deriving a local estimator for the superfluid density distribution, we find a decreased superfluid response in the first solvation layer. This effective normal fluid exhibits temperature dependence similar to that of a two-dimensional helium system.
To determine the state of spin polarization of the 3D electron gas at very low densities and zero temperature, we calculate the energy versus spin polarization using Diffusion Quantum Monte Carlo methods with backflow wavefunctions and twist averaged boundary conditions. We find a second order phase transition to a partially polarized phase at r_s = 50 \pm 2. The magnetic transition temperature is estimated using an effective mean field method, the Stoner model.
Path Integral Monte Carlo was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at $T=0.77 K$, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9 before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. Finally, a surface dispersion relation was calculated from imaginary-time density-density correlations.
We calculate the equation of state of dense deuterium with two ab initio simulations techniques, path integral Monte Carlo and density functional theory molecular dynamics, in the density range of 0.67 < rho < 1.60 g/cc. We derive the double shock Hugoniot and compare with the recent laser-driven double shock wave experiments by Mostovych et al. [1]. We find excellent agreement between the two types of microscopic simulations but a significant discrepancy with the laser-driven shock measurements.
Although quantum Monte Carlo is, in principal, an exact method for solving the Schroedinger equation, it is well-known that systems of Fermions still pose a challenge. Thus far all solutions to the "sign problem" remain inefficient (or wrong). The fixed-node approach, however, is efficient, and in many situations remains the best approach. If only we could find the exact nodes, or at least a systematic way to improve the nodes, we would, in effect, bypass the sign problem. Unfortunately, very little is known about wave function nodes, and a systematic study has never been attempted, despite the obvious consequences for improving quantum simulations that such knowledge might generate. In this paper we study the nodal surfaces of simple atomic systems.
Restricted path integral Monte Carlo simulations are used to calculate the equilibrium properties of hydrogen in the density and temperature range of $9.83 \times 10^{-4}\rm \leq ρ\leq 0.153 \rm gcm^{-3}$ and $5000 \leq T \leq 250 000 \rm K$. We test the accuracy of the pair density matrix and analyze the dependence on the system size, on the time step of the path integral and on the type of nodal surface. We calculate the equation of state and compare with other models for hydrogen valid in this regime. Further, we characterize the state of hydrogen and describe the changes from a plasma to an atomic and molecular liquid by analyzing the pair correlation functions and estimating the number of atoms and molecules present.
We develop and test Quantum Monte Carlo algorithms which use a``twist'' or a phase in the wave function for fermions in periodic boundary conditions. For metallic systems, averaging over the twist results in faster convergence to the thermodynamic limit than periodic boundary conditions for properties involving the kinetic energy with the same computational complexity. We determine exponents for the rate of convergence to the thermodynamic limit for the components of the energy of coulomb systems. We show results with twist averaged variational Monte Carlo on free particles, the Stoner model and the electron gas using Hartree-Fock, Slater-Jastrow, three-body and backflow wavefunction. We also discuss the use of twist averaging in the grand canonical ensemble, and numerical methods to accomplish the twist averaging.
We calculate cross sections for low energy elastic exciton-exciton scattering within the effective mass approximation. Unlike previous theoretical approaches, we give a complete, non-perturbative treatment of the four-particle scattering problem. Diffusion Monte Carlo is used to calculate the essentially exact energies of scattering states, from which phase shifts are determined. For the case of equal-mass electrons and holes, which is equivalent to positronium-positronium scattering, we find a_s = 2.1 a_x for scattering of singlet-excitons and a_s= 1.5 a_x for triplet-excitons, where a_x is the excitonic radius. The spin dependence of the cross sections arises from the spatial exchange symmetry of the scattering wavefunctions. A significant triplet-triplet to singlet-singlet scattering process is found, which is similar to reported effects in recent experiments and theory for excitons in quantum wells. We also show that the scattering length can change sign and diverge for some values of the mass ratio m_h/m_e, an effect not seen in previous perturbative treatments.
Using path integral Monte Carlo we simulate a 3D system of up to 1000 magnetic flux lines by mapping it onto a system of interacting bosons in (2+1)D. With increasing temperature we find a first order melting of flux lines from an ordered solid to an entangled liquid signalled by a finite entropy jump and sharp discontinuities in the defect density and the structure factor $S({\bf G})$ at the first reciprocal lattice vector. In the presence of a small number of strong columnar pins, we find that the crystal is transformed into a Bose glass phase with patches of crystalline order nucleated around the trapped vortices but with no overall positional or orientational order. This glassy phase melts into a defected entangled liquid through a continuous transition.
Using Path Integral Monte Carlo we have calculated exchange frequencies as electrons undergo ring exchanges in a ``clean'' 2d Wigner crystal as a function of density. The results show agreement with WKB calculations at very low density, but show a more rapid increase with density near melting. Remarkably, the exchange Hamiltonian closely resembles the measured exchanges in 2d He. Using the resulting multi-spin exchange model we find the spin Hamiltonian for r_s \leq 175 \pm 10 is a frustrated antiferromagnetic; its likely ground state is a spin liquid. For lower density the ground state will be ferromagnetic.
We have performed Path Integral Monte Carlo (PIMC) calculations to determine the effect of quenched disorder on the superfluid density of a dilute 3D hard sphere gas. The disorder was introduced by locating set of hard cylinders randomly inside the simulation cell. Our results indicate that the disorder leaves the superfluid critical temperature basically unchanged. Comparison to experiments of helium in Vycor is made.
We have calculated the exchange, correlation, and total electronic energy of a realistic InAs self-assembled quantum dot embedded in a GaAs matrix as a function of the number of electrons in the dot. The many-body interactions have been treated using the local spin density approximation (LSDA) to density functional theory (DFT) and diffusion quantum Monte Carlo (DMC), so that we may quantify the error introduced by LSDA. The comparison shows that the LSDA errors are about 1-2 meV per electron for the system considered. These errors are small enough to justify the use of LSDA calculations to test models of self-assembled dots against current experimental measurements.