Derivation of Green's function of a spin Calogero-Sutherland model by Uglov's method

Ryota Nakai, Yusuke Kato

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

The hole propagator of a spin 1/2 Calogero-Sutherland model is derived using Uglov's method, which maps the exact eigenfunctions of the model, called the 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 ψ + ψ on a Yangian Gelfand-Zetlin basis is transformed to the field annihilation operator ψ on gl2-Jack polynomials by the mapping. The resultant expression for the hole propagator for a 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 the spin Calogero-Sutherland model becomes equivalent to the dynamical colour correlation function of an SU(3) Haldane-Shastry model.

Original languageEnglish
Article number025209
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number2
DOIs
Publication statusPublished - 2009
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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