Analysis of the N=4 Hubbard ring using a counting operator

TL;DR

This paper develops theoretical tools using a counting operator to analyze the spectrum of the N=4 Hubbard ring, providing exact eigenvalues and insights into level crossings.

Contribution

It introduces three theorems for spectral analysis with a counting operator and applies them to the N=4 Hubbard ring, deriving exact eigenvalues.

Findings

Analytical eigenvalues for the N=4 Hubbard ring

Theorems describing level crossings in the spectrum

Application of counting operator to model Hamiltonians

Abstract

We prove three theorems about the use of a counting operator to study the spectrum of model Hamiltonians. We analytically calculate the eigenvalues of the Hubbard ring with four lattice positions and apply our theorems to describe the observed level crossings.