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arXiv:cond-mat/0301416 · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Quantum Monte Carlo algorithm for softcore boson systems

Jurij Šmakov, Kenji Harada, Naoki Kawashima

Published Oct 21, 2003• 3 citations
arXivHTMLPDF

Abstract

An efficient quantum Monte Carlo algorithm for the simulation of bosonic systems on a lattice in a grand canonical ensemble is proposed. It is based on the mapping of bosonic models to the spin models in the limit of the infinite total spin quantum number. It is demonstrated how this limit may be taken explicitly in the algorithm, eliminating the systematic errors. The efficiency of the algorithm is examined for the noninteracting lattice boson model and compared with the stochastic series expansion method with the heat-bath-type scattering probability of the random walker.

DOI
10.1103/physreve.68.046708

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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 approximately 400 bosons.
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