Existence of Different Intermediate Hamiltonians in Type A N-fold Supersymmetry II. The N=3 Case

TL;DR

This paper investigates the existence and classification of intermediate Hamiltonians in type A N=3 supersymmetric quantum systems, revealing various patterns and connections to parasupersymmetry and superalgebras.

Contribution

It provides a comprehensive classification of N=3 type A supersymmetric systems with intermediate Hamiltonians and explores their algebraic structures.

Findings

Multiple patterns of intermediate Hamiltonians in N=3 systems.

Complete classification restricted to elliptic type.

Realizations of parasupersymmetry and superalgebras.

Abstract

We continue the previous study on the existence of different intermediate Hamiltonians in type A N-fold supersymmetric systems and carry out an exhaustive investigation on the N=3 case. In contrast with the N=2 case, we find various patterns in the existence of intermediate Hamiltonians due to the presence of two different intermediate positions in a factorized type A 3-fold supercharge. In addition, all the N=3 models are strictly restricted to at most elliptic type, which enables us to make the complete classification of the systems which admit intermediate Hamiltonians. Finally, we show realizations of third-order parasupersymmetry and variant generalized 3-fold superalgebras by such systems.