Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry

TL;DR

This paper introduces a deformation of quantum Inozemtsev models that achieves quasi-exact solvability through N-fold supersymmetry, and presents a new method called pre-superpotential for solving such systems.

Contribution

It demonstrates how quantum Inozemtsev models can be deformed to exhibit quasi-exact solvability and introduces the pre-superpotential method for solving these models.

Findings

Quantum Inozemtsev models can be deformed to be quasi-exactly solvable.

These models possess N-fold supersymmetry.

The pre-superpotential method effectively identifies and solves quasi-exactly solvable systems.

Abstract

Inozemtsev models are classically integrable multi-particle dynamical systems related to Calogero-Moser models. Because of the additional q^6 (rational models) or sin^2(2q) (trigonometric models) potentials, their quantum versions are not exactly solvable in contrast with Calogero-Moser models. We show that quantum Inozemtsev models can be deformed to be a widest class of partly solvable (or quasi-exactly solvable) multi-particle dynamical systems. They posses N-fold supersymmetry which is equivalent to quasi-exact solvability. A new method for identifying and solving quasi-exactly solvable systems, the method of pre-superpotential, is presented.