dorsal/arxiv
View SchemaQuantum Monte Carlo method for the ground state of many-boson systems
| Authors | Wirawan Purwanto, Shiwei Zhang |
|---|---|
| Categories | |
| ArXiv ID | physics/0403146 |
| URL | https://arxiv.org/abs/physics/0403146 |
| DOI | 10.1103/PhysRevE.70.056702 |
| Journal | Phys. Rev. E 70, 056702 (2004) |
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. 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 non-interacting 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 ~ 400 bosons.
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"abstract": "We formulate a quantum Monte Carlo (QMC) method for calculating the ground\nstate of many-boson systems. The method is based on a field-theoretical\napproach, and is closely related to existing fermion auxiliary-field QMC\nmethods which are applied in several fields of physics. The ground-state\nprojection is implemented as a branching random walk in the space of permanents\nconsisting of identical single-particle orbitals. The method is in principle\nexact. We illustrate this method with a trapped atomic boson gas, where the\natoms interact via an attractive or repulsive contact two-body potential. We\nchoose as the single-particle basis a real-space grid. We compare with exact\nresults in small systems, and arbitrarily-sized systems of untrapped bosons\nwith attractive interactions in one dimension, where analytical solutions\nexist. We also compare with the corresponding Gross-Pitaevskii (GP) mean-field\ncalculations for trapped atoms, and discuss the close formal relation between\nour method and the GP approach. Our method provides a way to systematically\nimprove upon GP while using the same framework, capturing interaction and\ncorrelation effects with a stochastic, coherent ensemble of non-interacting\nsolutions. We discuss various algorithmic issues, including importance sampling\nand the back-propagation technique for computing observables, and illustrate\nthem with numerical studies. We show results for systems with up to N ~ 400\nbosons.",
"arxiv_id": "physics/0403146",
"authors": [
"Wirawan Purwanto",
"Shiwei Zhang"
],
"categories": [
"physics.comp-ph",
"cond-mat.soft",
"physics.atom-ph"
],
"doi": "10.1103/PhysRevE.70.056702",
"journal_ref": "Phys. Rev. E 70, 056702 (2004)",
"title": "Quantum Monte Carlo method for the ground state of many-boson systems",
"url": "https://arxiv.org/abs/physics/0403146"
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