A multispecies Calogero-Sutherland model

TL;DR

This paper introduces an exactly solvable multispecies Calogero-Sutherland model with specific parameter relations, revealing its ground state, density profiles, virial coefficients, and conformal field theory excitations, and discusses related anyon models.

Contribution

It provides an exact solution for a multispecies Calogero-Sutherland model under certain conditions, extending understanding of mutual statistics and low-energy excitations.

Findings

Exact ground state solutions on a circle and line with harmonic potential.

Derived one-particle densities using a generalized Thomas-Fermi approach.

Calculated second virial coefficients in high-temperature regime.

Abstract

Motivated by the concept of ideal mutual statistics, we study a multispecies Calogero-Sutherland model in which the interaction parameters and masses satisfy some specific relations. The ground state is exactly solvable if those relations hold, both on a circle and on a line with a simple harmonic potential. In the latter case, the one-particle densities can be obtained using a generalization of the Thomas-Fermi method. We calculate the second virial coefficients in the high temperature expansion for the pressure. We show that the low-energy excitations are the same as those of a Gaussian conformal field theory. Finally, we discuss similar relations between the statistics parameters and charges for a multispecies anyon model in a magnetic field.