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

2023/05/15 by Charles Arnal, Arnal, Charles, Louis Garrigue +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms #Nonlinear Photonic Systems #Quantum Physics (quant-ph) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2305.09026

openalex publication_date 2023/05/15 · openalex created_date 2023/05/18 · openalex updated_date 2026/07/28

Abstract

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.

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