A Family of Quasi-solvable Quantum Many-body Systems

TL;DR

This paper introduces a new family of quantum many-body systems that are quasi-solvable, encompassing various known models like Inozemtsev models, and classifies them based on algebraic and symmetry properties.

Contribution

The authors develop an algebraic method to construct and classify a broad family of quasi-solvable quantum many-body systems with permutation symmetry.

Findings

Includes rational, hyperbolic, and elliptic Inozemtsev models as special cases

Classifies models based on invariance properties

Constructs models with up to two-body interactions

Abstract

We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify these models under the consideration of invariance property. It turns out that this family includes the rational, hyperbolic (trigonometric) and elliptic Inozemtsev models as the particular cases.