Eigenvalues of the Anti-periodic Calogero - Sutherland Model

TL;DR

This paper analyzes the eigenvalues of the anti-periodic Calogero-Sutherland model by transforming its Hamiltonian into an upper triangular form, enabling straightforward computation of energy levels.

Contribution

It introduces a similarity transformation that simplifies the Hamiltonian and provides a matrix representation in an upper triangular form for the anti-periodic CSM.

Findings

Eigenvalues obtained from the diagonal elements of the transformed Hamiltonian.

The Hamiltonian can be represented in an upper triangular matrix form.

Simplification facilitates analysis of the model's spectral properties.

Abstract

The U(1) Calogero Sutherland Model (CSM) with anti-periodic boundary condition is studied. The Hamiltonian is reduced to a convenient form by similarity transformation. The matrix representation of the Hamiltonian acting on a partially ordered state space is obtained in an upper triangular form. Consequently the diagonal elements become the energy eigenvalues.