Generalized Calogero model in arbitrary dimensions

TL;DR

This paper introduces a new multispecies Calogero model in arbitrary dimensions, utilizing conformal symmetry to explicitly construct eigenstates, analyze the spectrum, and identify a universal critical point.

Contribution

The work extends Calogero models to D dimensions with multispecies interactions and provides explicit polynomial eigenstates and ladder operators using conformal SU(1,1) symmetry.

Findings

Explicit construction of polynomial eigenstates and energies

Identification of a universal critical point in the model

Development of ladder operators for collective states

Abstract

We define a new multispecies model of Calogero type in D dimensions with harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we indicate how to find the complete set of the states in Bargmann-Fock space. There are towers of states, with equidistant energy spectra in each tower. We explicitely construct all polynomial eigenstates, namely the center-of-mass states and global dilatation modes, and find their corresponding eigenenergies. We also construct ladder operators for these global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behavior. The above results are universal for all systems with underlying conformal SU(1,1) symmetry.