A New Construction of Quasi-solvable Quantum Many-body Systems of Deformed Calogero-Sutherland Type

TL;DR

This paper introduces a new multivariate generalization of monomial spaces, constructs quasi-solvable operators preserving these spaces, and identifies new quasi-solvable quantum many-body systems of deformed Calogero-Sutherland type, expanding the landscape beyond known models.

Contribution

It presents a novel type A' space, derives the most general quasi-solvable operators preserving it, and discovers new deformed Calogero-Sutherland models, extending previous classifications.

Findings

Identified new quasi-solvable models of deformed Calogero-Sutherland type.

Constructed the most general second-order quasi-solvable operators for type A' space.

Extended the framework to a multivariate generalization of type C monomial space.

Abstract

We make a new multivariate generalization of the type A monomial space of a single variable. It is different from the previously introduced type A space of several variables which is an sl(M+1) module, and we thus call it type A'. We construct the most general quasi-solvable operator of (at most) second-order which preserves the type A' space. Investigating directly the condition under which the type A' operators can be transformed to Schroedinger operators, we obtain the complete list of the type A' quasi-solvable quantum many-body systems. In particular, we find new quasi-solvable models of deformed Calogero-Sutherland type which are different from the Inozemtsev systems. We also examine a new multivariate generalization of the type C monomial space based on the type A' scheme.