Comment on: "On the characteristic polynomial of an effective Hamiltonian"

TL;DR

This paper clarifies that a recent method for analyzing effective Hamiltonians using characteristic polynomials was actually developed earlier, providing a clearer and more general approach, and compares implementations through a toy model.

Contribution

It reveals prior work on the characteristic polynomial method, offering a clearer, more general formulation and comparison of implementations.

Findings

Earlier development of the characteristic polynomial method

Comparison of two implementations using a toy model

Identification of the closest exceptional point

Abstract

We show that a method proposed recently, based on the characteristic polynomial of an effective Hamiltonian, had been developed several years earlier by other authors in a clearer and more general way. We outline both implementations of the approach and compare them by means of the calculation of the exceptional point closest to origin for a toy model.