Correlation functions of the BC Calogero-Sutherland model

TL;DR

This paper develops a formalism to analyze the correlation functions of the BC Calogero-Sutherland model, connecting it to random matrix theory and conformal field theory, and provides exact asymptotics and distribution results.

Contribution

It introduces a fermionic replica sigma-model approach for BC-type models, extending methods to derive exact asymptotics and distribution functions.

Findings

Derived exact asymptotics of the BC-CSM density profile.

Verified consistency with c=1 Gaussian conformal field theory.

Computed the distribution of the particle nearest to the reflection point.

Abstract

The BC-type Calogero-Sutherland model (CSM) is an integrable extension of the ordinary A-type CSM that possesses a reflection symmetry point. The BC-CSM is related to the chiral classes of random matrix ensembles (RMEs) in exactly the same way as the A-CSM is related to the Dyson classes. We first develop the fermionic replica sigma-model formalism suitable to treat all chiral RMEs. By exploiting ''generalized color-flavor transformation'' we then extend the method to find the exact asymptotics of the BC-CSM density profile. Consistency of our result with the c=1 Gaussian conformal field theory description is verified. The emerging Friedel oscillations structure and sum rules are discussed in details. We also compute the distribution of the particle nearest to the reflection point.