Improved scaling for quantum monte carlo on insulators

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dc.contributorVirginia Techen
dc.contributor.authorAhuja, Kapilen
dc.contributor.authorClark, Bryan K.en
dc.contributor.authorde Sturler, Ericen
dc.contributor.authorCeperley, David M.en
dc.contributor.authorKim, Jeongnimen
dc.contributor.departmentMathematicsen
dc.date.accessed2014-05-27en
dc.date.accessioned2014-05-28T18:35:07Zen
dc.date.available2014-05-28T18:35:07Zen
dc.date.issued2011en
dc.description.abstractQuantum Monte Carlo (QMC) methods are often used to calculate properties of many body quantum systems. The main cost of many QMC methods, for example, the variational Monte Carlo (VMC) method, is in constructing a sequence of Slater matrices and computing the ratios of determinants for successive Slater matrices. Recent work has improved the scaling of constructing Slater matrices for insulators so that the cost of constructing Slater matrices in these systems is now linear in the number of particles, whereas computing determinant ratios remains cubic in the number of particles. With the long term aim of simulating much larger systems, we improve the scaling of computing the determinant ratios in the VMC method for simulating insulators by using preconditioned iterative solvers. The main contribution of this paper is the development of a method to efficiently compute for the Slater matrices a sequence of preconditioners that make the iterative solver converge rapidly. This involves cheap preconditioner updates, an effective reordering strategy, and a cheap method to monitor instability of incomplete LU decomposition with threshold and pivoting (ILUTP) preconditioners. Using the resulting preconditioned iterative solvers to compute determinant ratios of consecutive Slater matrices reduces the scaling of QMC algorithms from O(n<sup>3</sup>) per sweep to roughly O(n<sup>2</sup>), where n is the number of particles, and a sweep is a sequence of n steps, each attempting to move a distinct particle. We demonstrate experimentally that we can achieve the improved scaling without increasing statistical errors. Our results show that preconditioned iterative solvers can dramatically reduce the cost of VMC for large(r) systems.en
dc.description.sponsorshipNSF NSF-EAR 0530643en
dc.description.sponsorshipMaterials Computation Center at the University of Illinoisen
dc.identifier.citationAhuja, K.; Clark, B. K.; De Sturler, E.; Ceperley, D. M.; Kim, J., "Improved scaling for quantum monte carlo on insulators," SIAM J. Sci. Comput., 33(4), 1837-1859, (2011). DOI: 10.1137/100805467en
dc.identifier.doihttps://doi.org/10.1137/100805467en
dc.identifier.issn1064-8275en
dc.identifier.urihttp://hdl.handle.net/10919/48153en
dc.identifier.urlhttp://epubs.siam.org/doi/abs/10.1137/100805467en
dc.language.isoen_USen
dc.publisherSiam Publicationsen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectvariational monte carloen
dc.subjectquantum monte carloen
dc.subjectsequence of linearen
dc.subjectsystemsen
dc.subjectpreconditioningen
dc.subjectupdating preconditionersen
dc.subjectkrylov subspaceen
dc.subjectmethodsen
dc.subjectpermuting large entriesen
dc.subjectlinear-systemsen
dc.subjectpreconditionersen
dc.subjectsimulationsen
dc.subjectalgorithmsen
dc.subjectmatricesen
dc.subjectmathematics, applieden
dc.titleImproved scaling for quantum monte carlo on insulatorsen
dc.title.serialSiam Journal on Scientific Computingen
dc.typeArticle - Refereeden

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