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arXiv:hep-th/0411231

Aspects of generalized Calogero model

Stjepan Meljanac, Andjelo Samsarov, Marijan Mileković

Published Nov 25, 2004• 0 citations
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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.

DOI
10.48550/arxiv.hep-th/0411231

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A multispecies model of Calogero type in D≥1D\geq 1D≥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.
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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\ncoefficients 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.\n\n