Calogero-Sutherland Model with Anti-periodic Boundary Conditions: Eigenvalues and Eigenstates

TL;DR

This paper analyzes the U(1) Calogero-Sutherland model with anti-periodic boundary conditions, deriving eigenvalues and eigenstates using similarity transformations, Young diagrams, and Jack polynomials.

Contribution

It introduces a method to obtain eigenvalues and eigenstates for the model with anti-periodic boundary conditions, utilizing a similarity transformation and symmetric polynomials.

Findings

Eigenvalues are obtained from the diagonal elements of the transformed Hamiltonian.

Eigenstates are constructed using Young diagrams and Jack symmetric polynomials.

The eigenstates are orthonormalized for further analysis.

Abstract

The U(1) Calogero Sutherland Model 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. The eigenstates are constructed using Young diagram and represented in terms of Jack symmetric polynomials. The eigenstates so obtained are orthonormalized.