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@ARTICLE{Sarkar:890687,
      author       = {Sarkar, Avik and Lee, Dean},
      title        = {{C}onvergence of {E}igenvector {C}ontinuation},
      journal      = {Physical review letters},
      volume       = {126},
      number       = {3},
      issn         = {1079-7114},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {FZJ-2021-01129},
      pages        = {032501},
      year         = {2021},
      abstract     = {Eigenvector continuation is a computational method that
                      finds the extremal eigenvalues and eigenvectors of a
                      Hamiltonian matrix with one or more control parameters. It
                      does this by projection onto a subspace of eigenvectors
                      corresponding to selected training values of the control
                      parameters. The method has proven to be very efficient and
                      accurate for interpolating and extrapolating eigenvectors.
                      However, almost nothing is known about how the method
                      converges, and its rapid convergence properties have
                      remained mysterious. In this Letter, we present the first
                      study of the convergence of eigenvector continuation. In
                      order to perform the mathematical analysis, we introduce a
                      new variant of eigenvector continuation that we call vector
                      continuation. We first prove that eigenvector continuation
                      and vector continuation have identical convergence
                      properties and then analyze the convergence of vector
                      continuation. Our analysis shows that, in general,
                      eigenvector continuation converges more rapidly than
                      perturbation theory. The faster convergence is achieved by
                      eliminating a phenomenon that we call differential folding,
                      the interference between nonorthogonal vectors appearing at
                      different orders in perturbation theory. From our analysis
                      we can predict how eigenvector continuation converges both
                      inside and outside the radius of convergence of perturbation
                      theory. While eigenvector continuation is a nonperturbative
                      method, we show that its rate of convergence can be deduced
                      from power series expansions of the eigenvectors. Our
                      results also yield new insights into the nature of
                      divergences in perturbation theory.},
      ddc          = {530},
      pnm          = {Nuclear Lattice Simulations $(jara0015_20200501)$},
      pid          = {$G:(DE-Juel1)jara0015_20200501$},
      typ          = {PUB:(DE-HGF)16},
      doi          = {10.1103/PhysRevLett.126.032501},
      url          = {https://juser.fz-juelich.de/record/890687},
}