Exactly and Quasi-Exactly Solvable Models on the Basis of $osp(2|1)$

TL;DR

This paper explores exactly and quasi-exactly solvable quantum models for spin-1/2 systems in one dimension using the hidden dynamical symmetry algebra $OSP(2|1)$, providing explicit spectra and new solvable classes.

Contribution

It introduces a framework based on the supergroup $OSP(2|1)$ for constructing and analyzing exactly and quasi-exactly solvable models in one-dimensional spin systems.

Findings

Explicit spectra for several solvable models

New classes of quasi-exactly solvable problems identified

Demonstration of the role of $OSP(2|1)$ symmetry in solvability

Abstract

The exactly and quasi-exactly solvable problems for spin one-half in one dimension on the basis of a hidden dynamical symmetry algebra of Hamiltonian are discussed. We take the supergroup, $OSP(2|1)$, as such a symmetry. A number of exactly solvable examples are considered and their spectrum are evaluated explicitly. Also, a class of quasi-exactly solvable problems on the basis of such a symmetry has been obtained.