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Title: Quantum Monte Carlo method for the ground state of many-boson systems

Abstract

We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. Any single-particle basis can be used, and the method is in principle exact. We illustrate this method with a trapped atomic boson gas, where the atoms interact via an attractive or repulsive contact two-body potential. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems and arbitrarily sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. We also compare with the corresponding Gross-Pitaevskii (GP) mean-field calculations for trapped atoms, and discuss the close formal relation between our method and the GP approach. Our method provides a way to systematically improve upon GP while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of noninteracting solutions. We discuss various algorithmic issues, including importance sampling and the back-propagation technique for computing observables,more » and illustrate them with numerical studies. We show results for systems with up to N{approx}400 bosons.« less

Authors:
;  [1]
  1. Department of Physics, The College of William and Mary, Williamsburg, Virginia 23187 (United States)
Publication Date:
OSTI Identifier:
20636886
Resource Type:
Journal Article
Journal Name:
Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Additional Journal Information:
Journal Volume: 70; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevE.70.056702; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1063-651X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ANALYTICAL SOLUTION; BOSONS; BRANCHING RATIO; COMPARATIVE EVALUATIONS; CORRELATIONS; FERMIONS; GROUND STATES; INFORMATION THEORY; MEAN-FIELD THEORY; MONTE CARLO METHOD; NUMERICAL ANALYSIS; POTENTIALS; QUANTUM MECHANICS; RANDOMNESS; SAMPLING; TRAPPING; TWO-BODY PROBLEM

Citation Formats

Purwanto, Wirawan, and Shiwei, Zhang. Quantum Monte Carlo method for the ground state of many-boson systems. United States: N. p., 2004. Web. doi:10.1103/PhysRevE.70.056702.
Purwanto, Wirawan, & Shiwei, Zhang. Quantum Monte Carlo method for the ground state of many-boson systems. United States. doi:10.1103/PhysRevE.70.056702.
Purwanto, Wirawan, and Shiwei, Zhang. Mon . "Quantum Monte Carlo method for the ground state of many-boson systems". United States. doi:10.1103/PhysRevE.70.056702.
@article{osti_20636886,
title = {Quantum Monte Carlo method for the ground state of many-boson systems},
author = {Purwanto, Wirawan and Shiwei, Zhang},
abstractNote = {We formulate a quantum Monte Carlo (QMC) method for calculating the ground state of many-boson systems. The method is based on a field-theoretical approach, and is closely related to existing fermion auxiliary-field QMC methods which are applied in several fields of physics. The ground-state projection is implemented as a branching random walk in the space of permanents consisting of identical single-particle orbitals. Any single-particle basis can be used, and the method is in principle exact. We illustrate this method with a trapped atomic boson gas, where the atoms interact via an attractive or repulsive contact two-body potential. We choose as the single-particle basis a real-space grid. We compare with exact results in small systems and arbitrarily sized systems of untrapped bosons with attractive interactions in one dimension, where analytical solutions exist. We also compare with the corresponding Gross-Pitaevskii (GP) mean-field calculations for trapped atoms, and discuss the close formal relation between our method and the GP approach. Our method provides a way to systematically improve upon GP while using the same framework, capturing interaction and correlation effects with a stochastic, coherent ensemble of noninteracting solutions. We discuss various algorithmic issues, including importance sampling and the back-propagation technique for computing observables, and illustrate them with numerical studies. We show results for systems with up to N{approx}400 bosons.},
doi = {10.1103/PhysRevE.70.056702},
journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},
issn = {1063-651X},
number = 5,
volume = 70,
place = {United States},
year = {2004},
month = {11}
}