Answer to the comment on "On the characteristic polynomial of an effective Hamiltonian''

TL;DR

This paper clarifies differences between their effective Hamiltonian solution method based on the characteristic polynomial and a prior resummation approach, addressing claims of prior development.

Contribution

The authors distinguish their method from previous work, highlighting novel aspects in their approach to effective Hamiltonians.

Findings

Identified key differences between the two methods.

Clarified the novelty of their solution approach.

Refuted claims of prior development by Fried and Ezra.

Abstract

In a recent comment by Fern\'{a}ndez, it has been argued that our solution method of an effective Hamiltonian based on the characteristic polynomial [Phys. Lett. A 443 (2022) 128215] had been developed several years earlier by Fried and Ezra [J. Chem. Phys. 90 (1989) 6378]. We show here several important differences between our treatment and the resummation method proposed previously by Fried and Ezra.