dorsal/arxiv
View SchemaWorm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations
| Authors | M. Boninsegni, N. V. Prokof'ev, B. V. Svistunov |
|---|---|
| Categories | |
| ArXiv ID | physics/0605225 |
| URL | https://arxiv.org/abs/physics/0605225 |
| DOI | 10.1103/PhysRevE.74.036701 |
| Journal | Phys. Rev. E 74, 036701 (2006) |
Abstract
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 helium-four in two and three dimensions, as well as the calculation of the chemical potential of solid helium-four.
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"abstract": "A detailed description is provided of a new Worm Algorithm, enabling the\naccurate computation of thermodynamic properties of quantum many-body systems\nin continuous space, at finite temperature. The algorithm is formulated within\nthe general Path Integral Monte Carlo (PIMC) scheme, but also allows one to\nperform quantum simulations in the grand canonical ensemble, as well as to\ncompute off-diagonal imaginary-time correlation functions, such as the\nMatsubara Green function, simultaneously with diagonal observables. Another\nimportant innovation consists of the expansion of the attractive part of the\npairwise potential energy into elementary (diagrammatic) contributions, which\nare then statistically sampled. This affords a complete microscopic account of\nthe long-range part of the potential energy, while keeping the computational\ncomplexity of all updates independent of the size of the simulated system. The\ncomputational scheme allows for efficient calculations of the superfluid\nfraction and off-diagonal correlations in space-time, for system sizes which\nare orders of magnitude larger than those accessible to conventional PIMC. We\npresent illustrative results for the superfluid transition in bulk liquid\nhelium-four in two and three dimensions, as well as the calculation of the\nchemical potential of solid helium-four.",
"arxiv_id": "physics/0605225",
"authors": [
"M. Boninsegni",
"N. V. Prokof\u0027ev",
"B. V. Svistunov"
],
"categories": [
"physics.comp-ph",
"cond-mat.stat-mech"
],
"doi": "10.1103/PhysRevE.74.036701",
"journal_ref": "Phys. Rev. E 74, 036701 (2006)",
"title": "Worm Algorithm and Diagrammatic Monte Carlo: A New Approach to Continuous-Space Path Integral Monte Carlo Simulations",
"url": "https://arxiv.org/abs/physics/0605225"
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