Improving procedure for the reconstruction of an effective secular equation

TL;DR

This paper introduces an improved method for reconstructing the secular equation of an effective Hamiltonian, utilizing a relative characteristic polynomial to simplify calculations, especially for large P-space dimensions.

Contribution

The paper presents a novel approach using a relative characteristic polynomial to simplify the effective-secular-equation reconstruction process.

Findings

Simplified effective-secular-equation for large P-space

Enhanced convenience and effectiveness in reconstruction

Equivalent results to traditional methods

Abstract

The usual implement procedure for the reconstruction of secular equation for an effective Hamiltonian has been discussed and improved. A relative characteristic polynomial has been introduced for the effective Hamiltonian, to obtain a simplified effective-secular-equation which is equivalent to the one obtained in the usual reconstruction procedure but shows great convenience and effectiveness, especially when the $P$-space dimension is large.