Entanglement Entropy in the Calogero-Sutherland Model

TL;DR

This paper derives exact expressions for entanglement entropy in the Calogero-Sutherland model using Jack polynomials, revealing an upper bound linked to fractional exclusion statistics.

Contribution

It introduces a novel method to compute entanglement entropy exactly in the Calogero-Sutherland model leveraging duality of Jack polynomials.

Findings

Exact formulas for reduced density matrix and entanglement entropy.

An upper bound for entanglement entropy related to fractional exclusion statistics.

Insight into the entanglement structure of the Calogero-Sutherland model.

Abstract

We investigate the entanglement entropy between two subsets of particles in the ground state of the Calogero-Sutherland model. By using the duality relations of the Jack symmetric polynomials, we obtain exact expressions for both the reduced density matrix and the entanglement entropy in the limit of an infinite number of particles traced out. From these results, we obtain an upper bound value of the entanglement entropy. This upper bound has a clear interpretation in terms of fractional exclusion statistics.