Rayleigh-Schrodinger QDPT for Hermitian intermediate Hamiltonians by the shift technique

Abstract

A general approach to the construction of Rayleigh-Schrodinger-like perturbative expansions for Hermitian intermediate Hamiltonians using the shift technique is proposed. The shift operator depends on the projector onto the subspace spanned by the 'main' eigenvectors of the intermediate Hamiltonian which should be determined iteratively for a given PT order. The intruder state problem can be completely eliminated by an appropriate choice of an intermediate space and shift parameters without introducing any additional perturbation. Numerical examples are reported in order to demonstrate the convergency properties and approximate size consistency of the novel method.