A multispecies Calogero model

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.

arXiv comment16 pages, no figures, LateX, enlarged version that appeared in Phys.Lett.B

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• Universal properties of conformal quantum many-body systems
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• Solitons in the Calogero model for distinguishable particles
• Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
• Explicit formulas for the eigenfunctions of the N-body Calogero model
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• Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
• Matrix oscillator and Laughlin Hall states
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• Solutions of coupled BPS equations for two-family Calogero and matrix models
• Calogero Model(s) and Deformed Oscillators
• Parent Hamiltonians of Jastrow Wavefunctions