Coefficients of almost-degenerate density matrix perturbation theory for eigenvalue problems

We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become singular because inverses of differences between eigenvalues arise...

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Bibliographic Details
Published in:arXiv.org 2023-07
Main Authors: Arnal, Charles, Garrigue, Louis
Format: Article
Language:English
Subjects:
Coefficients
Density
Eigenvalues
Perturbation theory
Projectors
Online Access:Get full text
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Summary:We investigate almost-degenerate perturbation theory of eigenvalue problems, using spectral projectors, also named density matrices. When several eigenvalues are close to each other, the coefficients of the perturbative series become singular because inverses of differences between eigenvalues arise as some factors. We remove those artificial singularities in the expressions of the coefficients of the series, allowing eigenvalue gaps to be arbitrarily small and even vanishing in the resulting formulas.
ISSN:2331-8422