Quasi-solvability of Calogero-Sutherland model with Anti-periodic Boundary Condition

TL;DR

This paper investigates the integrability and quasi-solvability of the U(1) Calogero-Sutherland model with anti-periodic boundary conditions, revealing its invariance properties and construction of commuting operators.

Contribution

It demonstrates the quasi-solvability of the model by transforming the Hamiltonian and constructing commuting momentum operators, extending understanding of boundary condition effects.

Findings

Hamiltonian is integrable with constructed commuting operators

Function space remains invariant under these operators

Model exhibits quasi-solvability due to invariance properties

Abstract

The U(1) Calogero-Sutherland Model with anti-periodic boundary condition is studied. This model is obtained by applying a vertical magnetic field perpendicular to the plane of one dimensional ring of particles. The trigonometric form of the Hamiltonian is recast by using a suitable similarity transformation. The transformed Hamiltonian is shown to be integrable by constructing a set of momentum operators which commutes with the Hamiltonian and amongst themselves. The function space of monomials of several variables remains invariant under the action of these operators. The above properties imply the quasi-solvability of the Hamiltonian under consideration.