Exceptional Points, Nonnormal Matrices, Hierarchy of Spin Matrices and an Eigenvalue Problem

TL;DR

This paper investigates exceptional points in non-Hermitian spin Hamiltonians, analyzing nonnormal matrices and their eigenvalue problems in finite-dimensional Hilbert spaces for various spin values.

Contribution

It introduces a study of exceptional points in non-Hermitian spin Hamiltonians using nonnormal matrices, expanding understanding of their eigenvalue structures.

Findings

Identification of exceptional points in spin matrices

Analysis of nonnormal operator properties

Eigenvalue problem characterization for different spins

Abstract

Exceptional points of a class of non-hermitian Hamilton operators $\hat H$ of the form $\hat H=\hat H_0+i\hat H_1$ are studied, where $\hat H_0$ and $\hat H_1$ are hermitian operators. Finite dimensional Hilbert spaces are considered. The linear operators $\hat H_0$ and $\hat H_1$ are given by spin matrices for spin $s=1/2,1,3/2,\dots$. Since the linear operators studied are nonnormal, properties of such operators are described.