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dc.contributor.authorShepherd, James J.
Scuseria, Gustavo E.
Spencer, James S.
dc.date.accessioned 2016-01-29T20:03:39Z
dc.date.available 2016-01-29T20:03:39Z
dc.date.issued 2014
dc.identifier.citation Shepherd, James J., Scuseria, Gustavo E. and Spencer, James S.. "Sign problem in full configuration interaction quantum Monte Carlo: Linear and sublinear representation regimes for the exact wave function." Physical Review B, 90, no. 15 (2014) American Physical Society: 155130. http://dx.doi.org/10.1103/PhysRevB.90.155130.
dc.identifier.urihttps://hdl.handle.net/1911/88274
dc.description.abstract We investigate the sign problem for full configuration interaction quantum Monte Carlo (FCIQMC), a stochastic algorithm for finding the ground-state solution of the Schrödinger equation with substantially reduced computational cost compared with exact diagonalization. We find k-space Hubbard models for which the solution is yielded with storage that grows sublinearly in the size of the many-body Hilbert space, in spite of using a wave function that is simply a linear combination of states. The FCIQMC algorithm is able to find this sublinear scaling regime without bias and with only a choice of the Hamiltonian basis. By means of a demonstration we solve for the energy of a 70-site half-filled system (with a space of 1038 determinants) in 250 core hours, substantially quicker than the ∼1036 core hours that would be required by exact diagonalization. This is the largest space that has been sampled in an unbiased fashion. The challenge for the recently developed FCIQMC method is made clear: Expand the sublinear scaling regime while retaining exact-on-average accuracy. We comment upon the relationship between this and the scaling law previously observed in the initiator adaptation (i-FCIQMC). We argue that our results change the landscape for the development of FCIQMC and related methods.
dc.language.iso eng
dc.publisher American Physical Society
dc.rights This article is available under the terms of the Creative Commons Attribution 3.0 License.
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/
dc.title Sign problem in full configuration interaction quantum Monte Carlo: Linear and sublinear representation regimes for the exact wave function
dc.type Journal article
dc.contributor.funder U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Heavy Element Chemistry Program
dc.contributor.funder Welch Foundation
dc.citation.journalTitle Physical Review B
dc.citation.volumeNumber 90
dc.citation.issueNumber 15
dc.type.dcmi Text
dc.identifier.doihttp://dx.doi.org/10.1103/PhysRevB.90.155130
dc.identifier.grantID DE-FG02-04ER15523 (U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Heavy Element Chemistry Program)
dc.identifier.grantID C-0036 (Welch Foundation)
dc.type.publication publisher version
dc.citation.firstpage 155130


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