On the characteristic polynomial of an effective Hamiltonian

TL;DR

This paper explores the properties of the characteristic polynomial of an effective Hamiltonian, showing it has better analytical features for perturbation calculations and constructing a form with matching singularities.

Contribution

It introduces a form of effective Hamiltonian sharing the same singularities as the characteristic polynomial, enhancing perturbation analysis.

Findings

Characteristic polynomial has superior convergence properties.

Constructed an effective Hamiltonian with identical singularities.

Improved perturbation calculation methods.

Abstract

The characteristic polynomial of the effective Hamiltonian for a general model has been discussed. It is found that, compared with the associated energy eigenvalues, this characteristic polynomial generally has better analytical properties and larger convergence radius when being expanded in powers of the interaction parameter, and hence is more suitable for a perturbation calculation. A form of effective Hamiltonian which has the same singularities (branch points) as such characteristic polynomial has also been constructed.