Critical Properties of the Calogero-Sutherland Model with Boundaries

TL;DR

This paper investigates the boundary effects on the critical properties of the $BC_N$-type Calogero-Sutherland model, demonstrating its low-energy behavior aligns with boundary conformal field theory and classifies it as a chiral Luttinger liquid.

Contribution

It provides a detailed analysis of the finite-size spectrum and boundary effects of the $BC_N$-CS model, linking it to boundary conformal field theory and Luttinger liquids.

Findings

Finite-size corrections reveal boundary contributions.

Low-energy behavior described by $c=1$ boundary CFT.

Model classified as a chiral Tomonaga-Luttinger liquid.

Abstract

Critical properties of the Calogero-Sutherland model of $BC_N$-type ($BC_N$-CS model) are studied. Using the asymptotic Bethe-ansatz spectrum of the $BC_N$-CS model, we calculate finite-size corrections in the energy spectrum. Since the $BC_N$-CS model does not possess translational invariance, the finite-size spectrum acquires the contributions coming from ``boundaries''. We show that the low-energy critical behavior of the model is described by $c=1$ boundary conformal field theory. Thus the universality class of the model is identified as a chiral Tomonaga-Luttinger liquid.