Collective Field Description of Spin Calogero-Sutherland Models

Abstract

Using the collective field technique, we give the description of the spin Calogero-Sutherland Model (CSM) in terms of free bosons. This approach can be applicable for arbitrary coupling constant and provides the bosonized Hamiltonian of the spin CSM. The boson Fock space can be identified with the Hilbert space of the spin CSM in the large $N$ limit. We show that the eigenstates corresponding to the Young diagram with a single row or column are represented by the vertex operators. We also derive a dual description of the Hamiltonian and comment on the construction of the general eigenstates.

arXiv comment14 pages, one figure, LaTeX, with minor corrections

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Cited by in corpus (9)

• The Calogero-Sutherland Model and Polynomials with Prescribed Symmetry
• Collective Field Theory for Quantum Hall States
• Cold Fermi-gas with long range interaction in a harmonic trap
• Nonlinear dynamics of spin and charge in spin-Calogero model
• On Spin Calogero-Moser system at infinity
• Fermionic limit of the Calogero-Sutherland system
• Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics
• On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta
• Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system