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      Convergence without resummation: an iterative approach to perturbative eigenvalue problems

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          Abstract

          We compute the eigenvectors of perturbed linear operators through fixed-point iteration instead of power series expansions. The method is elementary, explicit, and convergent under more general conditions than conventional Rayleigh-Schr\"odinger theory (which arises as a particular limiting case). We illustrate this "iterative perturbation theory" (IPT) with several challenging ground state computations, including even anharmonic oscillators, the hydrogenic Zeeman problem, and the Herbst-Simon Hamiltonian with finite ground state energy but vanishing Rayleigh-Schr\"odinger expansion. In all cases, we find that, with a suitable partitioning of the Hamiltonian, IPT converges to the correct eigenvector (hence eigenvalue) without restrictions on the coupling constant and without the need for any resummation procedure.

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          Author and article information

          Journal
          11 May 2021
          Article
          2105.04972
          056aee19-be47-4188-97cb-a2f806c2fe16

          http://creativecommons.org/licenses/by/4.0/

          History
          Custom metadata
          6 pages, 5 figures
          quant-ph cond-mat.other hep-th math-ph math.MP

          Mathematical physics,Condensed matter,Quantum physics & Field theory,High energy & Particle physics,Mathematical & Computational physics

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