Eigenvector Continuation with Subspace Learning

Frame, Dillon; He, Rongzheng; Ipsen, Ilse; Lee, Daniel; Lee, Dean; Rrapaj, Ermal

doi:10.1103/physrevlett.121.032501

Eigenvector Continuation with Subspace Learning

Journal Article · Tue Jul 17 00:00:00 EDT 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.121.032501· OSTI ID:1541342

Frame, Dillon ^[1]; He, Rongzheng ^[2]; Ipsen, Ilse ^[3]; Lee, Daniel ^[4]; Lee, Dean ^[2]; Rrapaj, Ermal ^[5]

Michigan State Univ., East Lansing, MI (United States). Facility for Rare Isotope Beams. Dept. of Physics and Astronomy; North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics; DOE/OSTI
Michigan State Univ., East Lansing, MI (United States). Facility for Rare Isotope Beams. Dept. of Physics and Astronomy; North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics
North Carolina State Univ., Raleigh, NC (United States). Dept. of Mathematics
Univ. of Pennsylvania, Philadelphia, PA (United States). School of Engineering and Applied Science
Univ. of Guelph, ON (Canada). Dept. of Physics

A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous efficient methods developed for this task, but they generally fail when some control parameter in the Hamiltonian matrix exceeds some threshold value. In this Letter we present a new technique called eigenvector continuation that can extend the reach of these methods. The key insight is that while an eigenvector resides in a linear space with enormous dimensions, the eigenvector trajectory generated by smooth changes of the Hamiltonian matrix is well approximated by a very low-dimensional manifold. We prove this statement using analytic function theory and propose an algorithm to solve for the extremal eigenvectors. We benchmark the method using several examples from quantum many-body theory.

View Accepted Manuscript (DOE)

Research Organization:: North Carolina State Univ., Raleigh, NC (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-03ER41260

OSTI ID:: 1541342

Alternate ID(s):: OSTI ID: 1460593

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 3 Vol. 121; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Global Sensitivity Analysis of Bulk Properties of an Atomic Nucleus Ekström, Andreas; Hagen, Gaute Physical Review Letters, Vol. 123, Issue 25 https://doi.org/10.1103/PhysRevLett.123.252501	journal	December 2019
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Global sensitivity analysis of bulk properties of an atomic nucleus Ekström, Andreas; Hagen, Gaute arXiv https://doi.org/10.48550/arxiv.1910.02922	text	January 2019

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