Worm algorithm and diagrammatic Monte Carlo: A new approach to continuous-space path integral Monte Carlo simulations
- Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1 (Canada)
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 (United States)
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 a 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.
- OSTI ID:
- 21072318
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 74, Issue 3; Other Information: DOI: 10.1103/PhysRevE.74.036701; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
36 MATERIALS SCIENCE
ALGORITHMS
COMPUTERIZED SIMULATION
CORRELATION FUNCTIONS
CORRELATIONS
GREEN FUNCTION
HCP LATTICES
HELIUM
HELIUM 4
LIQUIDS
MANY-BODY PROBLEM
MONTE CARLO METHOD
PATH INTEGRALS
POTENTIAL ENERGY
POTENTIALS
QUANTUM MECHANICS
SOLIDS
SPACE
SPACE-TIME
SUPERFLUIDITY
THERMODYNAMIC PROPERTIES