Derivation of Green's Function of Spin Calogero-Sutherland Model by Uglov's Method
arXiv:0809.2673 · doi:10.1088/1751-8113/42/2/025209
Abstract
Hole propagator of spin 1/2 Calogero-Sutherland model is derived using Uglov's method, which maps the exact eigenfunctions of the model, called Yangian Gelfand-Zetlin basis, to a limit of Macdonald polynomials (gl_2-Jack polynomials). To apply this mapping method to the calculation of 1-particle Green's function, we confirm that the sum of the field annihilation operator on Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator on gl_2-Jack polynomials by the mapping. The resultant expression for hole propagator for finite-size system is written in terms of renormalized momenta and spin of quasi-holes and the expression in the thermodynamic limit coincides with the earlier result derived by another method. We also discuss the singularity of the spectral function for a specific coupling parameter where the hole propagator of spin Calogero-Sutherland model becomes equivalent to dynamical colour correlation function of SU(3) Haldane-Shastry model.
36 pages, 8 figures
References in corpus (6)
- Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model
- Dynamic structure factor of the Calogero-Sutherland model
- Exact dynamical structure factor of the degenerate Haldane-Shastry model
- Exact Dynamics of the SU(K) Haldane-Shastry Model
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