Relativistic Calogero-Sutherland Model: Spin Generalization, Quantum Affine Symmetry and Dynamical Correlation Functions

TL;DR

This paper extends the relativistic Calogero-Sutherland model to include spin, revealing quantum affine symmetry, and provides exact calculations of correlation functions, showing the model exhibits Luttinger liquid behavior and fractional exclusion statistics.

Contribution

It introduces a spin generalization of the relativistic Calogero-Sutherland model using affine Hecke algebra and analyzes its quantum affine symmetry and correlation functions.

Findings

Exact diagonalization using Macdonald polynomials

Correlation functions evaluated explicitly

Model exhibits Luttinger liquid and fractional exclusion statistics behaviors

Abstract

Spin generalization of the relativistic Calogero-Sutherland model is constructed by using the affine Hecke algebra and shown to possess the quantum affine symmetry $\uqglt$. The spin-less model is exactly diagonalized by means of the Macdonald symmetric polynomials. The dynamical density-density correlation function as well as one-particle Green function are evaluated exactly. We also investigate the finite-size scaling of the model and show that the low-energy behavior is described by the $C=1$ Gaussian theory. The results indicate that the excitations obey the fractional exclusion statistics and exhibit the Tomonaga-Luttinger liquid behavior as well.