A multispecies Calogero model

TL;DR

This paper analyzes a multispecies Calogero model with complex interactions, revealing its spectrum, degeneracies, and symmetry properties, and identifying a universal critical point where the model exhibits singular behavior.

Contribution

It introduces an algebraic approach to construct eigenstates and uncovers the SU(2) symmetry responsible for degeneracies in the spectrum.

Findings

Spectrum is linear in quantum numbers

Higher-energy levels are degenerate

Identifies a universal critical point

Abstract

We study a multispecies one-dimensional Calogero model with two- and three-body interactions. Using an algebraic approach (Fock space analysis), we construct ladder operators and find infinitely many, but not all, exact eigenstates of the model Hamiltonian. Besides the ground state energy, we deduce energies of the excited states. It turns out that the spectrum is linear in quantum numbers and that the higher-energy levels are degenerate. The dynamical symmetry responsible for degeneracy is SU(2). We also find the universal critical point at which the model exhibits singular behaviour. Finally, we make contact with some special cases mentioned in the literature.