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

Ryota Nakai, Yusuke Kato

研究成果: Article査読

2 被引用数 (Scopus)


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.

ジャーナルJournal of Physics A: Mathematical and Theoretical
出版ステータスPublished - 2009

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 統計学および確率
  • モデリングとシミュレーション
  • 数理物理学
  • 物理学および天文学(全般)


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