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Title: Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations

Abstract

We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC simulations. As an illustrative application of the method, we simulate the superfluid transition of {sup 4}He in two dimensions.

Authors:
 [1];  [1];  [2];  [3];  [2];  [4];  [3]
  1. Department of Physics, University of Alberta, Edmonton, Alberta T6G 2J1 (Canada)
  2. (United States)
  3. (Russian Federation)
  4. Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 (United States)
Publication Date:
OSTI Identifier:
20777030
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 96; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevLett.96.070601; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE; ALGORITHMS; COMPUTERIZED SIMULATION; CORRELATIONS; HELIUM 4; LATTICE FIELD THEORY; MANY-BODY PROBLEM; MONTE CARLO METHOD; PATH INTEGRALS; SUPERFLUIDITY; THERMODYNAMIC PROPERTIES

Citation Formats

Boninsegni, Massimo, Prokof'ev, Nikolay, Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, Russian Research Center 'Kurchatov Institute', 123182 Moscow, Department of Physics, Cornell University, Ithaca, New York 14850, Svistunov, Boris, and Russian Research Center 'Kurchatov Institute', 123182 Moscow. Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations. United States: N. p., 2006. Web. doi:10.1103/PhysRevLett.96.070601.
Boninsegni, Massimo, Prokof'ev, Nikolay, Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, Russian Research Center 'Kurchatov Institute', 123182 Moscow, Department of Physics, Cornell University, Ithaca, New York 14850, Svistunov, Boris, & Russian Research Center 'Kurchatov Institute', 123182 Moscow. Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations. United States. doi:10.1103/PhysRevLett.96.070601.
Boninsegni, Massimo, Prokof'ev, Nikolay, Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, Russian Research Center 'Kurchatov Institute', 123182 Moscow, Department of Physics, Cornell University, Ithaca, New York 14850, Svistunov, Boris, and Russian Research Center 'Kurchatov Institute', 123182 Moscow. Fri . "Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations". United States. doi:10.1103/PhysRevLett.96.070601.
@article{osti_20777030,
title = {Worm Algorithm for Continuous-Space Path Integral Monte Carlo Simulations},
author = {Boninsegni, Massimo and Prokof'ev, Nikolay and Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 and Russian Research Center 'Kurchatov Institute', 123182 Moscow and Department of Physics, Cornell University, Ithaca, New York 14850 and Svistunov, Boris and Russian Research Center 'Kurchatov Institute', 123182 Moscow},
abstractNote = {We present a new approach to path integral Monte Carlo (PIMC) simulations based on the worm algorithm, originally developed for lattice models and extended here to continuous-space many-body systems. The scheme allows for efficient computation of thermodynamic properties, including winding numbers and off-diagonal correlations, for systems of much greater size than that accessible to conventional PIMC simulations. As an illustrative application of the method, we simulate the superfluid transition of {sup 4}He in two dimensions.},
doi = {10.1103/PhysRevLett.96.070601},
journal = {Physical Review Letters},
number = 7,
volume = 96,
place = {United States},
year = {Fri Feb 24 00:00:00 EST 2006},
month = {Fri Feb 24 00:00:00 EST 2006}
}
  • A detailed description is provided of a new worm algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the general path integral Monte Carlo (PIMC) scheme, but also allows one to perform quantum simulations in the grand canonical ensemble, as well as to compute off-diagonal imaginary-time correlation functions, such as the Matsubara Green function, simultaneously with diagonal observables. Another important innovation consists of the expansion of the attractive part of the pairwise potential energy into elementary (diagrammatic) contributions, which are then statistically sampled. This affords amore » complete microscopic account of the long-range part of the potential energy, while keeping the computational complexity of all updates independent of the size of the simulated system. The computational scheme allows for efficient calculations of the superfluid fraction and off-diagonal correlations in space-time, for system sizes which are orders of magnitude larger than those accessible to conventional PIMC. We present illustrative results for the superfluid transition in bulk liquid {sup 4}He in two and three dimensions, as well as the calculation of the chemical potential of hcp {sup 4}He.« less
  • In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique formore » efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed.« less
  • The (1,1,1)-surfaces of bulk solid molecular hydrogen have been studied at temperatures between 0.5 K and 1.3 K, using path integral Monte Carlo. A general method is introduced for constructing an external potential to represent the tail correction for an arbitrary heterogeneous layered bulk substrate-adsorbate system. The authors compute density profiles parallel and perpendicular to the free H[sub 2] surface, total energies, and the surface tension. The structure of partial (not completely filled) surface layers is investigated and found liquid for some filling fractions. Quantum exchange of H[sub 2] molecules at the free surface is observed and the possibility ofmore » superfluidity in a surface layer of H[sub 2] is discussed.« less
  • Atomatically thin [sup 4]He films of up to three monolayers on molecular hydrogen (1,1,1) surfaces are studied at T = 0.5 K, using path integral Monte Carlo. The authors compute the binding energy of [sup 4]He to the H[sub 2] substrate as a function of [sup 4]He coverage and obtain evidence of the prewetting transition. Density profiles perpendicular to the [sup 4]He-H[sub 2] interface are obtained, as well as the zero point motion and effective mass of [sup 4]He parallel to the substrate surface. The superfluid density of [sup 4]He vs. coverage is calculated, and the intermediate scattering function ismore » computed, from which they estimate the speed of third sound. Finally, they calculate the vorticity-vorticity correlation function.« less
  • Two algorithms which mix a staging procedure with a conventional Metropolis importance sampling are derived. Their applicability in simulating the thermal equilibrium properties of quantum systems is tested in three systems: a quantum free particle, an electron in a hard spheres crystal, and an electron in helium. We conclude that the two algorithms are generally more efficient than others used previously for the same systems, with a further advantage of being machine independent and able to deal with both hard core and smooth potentials. We also show that it is possible to model the properties of the electron in heliummore » with a hard core potential for the interaction of the electron with helium as well as the helium-helium interaction.« less