Aspects of generalized Calogero model

TL;DR

This paper constructs a multispecies Calogero model in multiple dimensions, incorporating harmonic, two-body, and three-body interactions, and identifies a universal critical point with singular behavior.

Contribution

It introduces a generalized multispecies Calogero model in higher dimensions with exact eigenenergies and analyzes its critical behavior using conformal algebra.

Findings

Exact eigenenergies for a class of states derived

Universal critical point identified with singular behavior

Model includes harmonic, two-body, and three-body interactions

Abstract

A multispecies model of Calogero type in $D\geq 1$ dimensions is constructed. The model includes harmonic, two-body and three-body interactions. Using the underlying conformal SU(1,1) algebra, we find the exact eigenenergies corresponding to a class of the exact global collective states. Analysing corresponding Fock space, we detect the universal critical point at which the model exhibits singular behaviour.