$gl(n|m)$ color Calogero-Sutherland models and Super Yangian Algebra

Abstract

A supersymmetric extension of the color Calogero-Sutherland model is considered based on the Yangian $Y(gl(n|m))$. The algebraic structure of the model is discussed in some details. We show that the commuting conserved quantities can be generated from the super-quantum determinant, thus establishing the integrability of the model. In addition, rational limit of the model is studied where the Yangian symmetry degenerates into a super loop algebra.

15 pages, standard Latex file

References in corpus (4)

• Yang-Baxter equation in spin chains with long range interactions
• Lattice Integrable Systems of Haldane-Shastry Type
• Integrable Systems for Particles with Internal Degrees of Freedom
• The Calogero Model - Anyonic Representation, Fermionic Extension and Supersymmetry

Cited by in corpus (12)

• Gauss Decomposition of the Yangian Y(gl_{m|n})
• Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain
• Boson-fermion duality in SU(m|n) supersymmetric Haldane-Shastry spin chain
• Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• The Algebraic Structure of the $gl(n|m)$ Color Calogero-Sutherland Models
• Aspects of Integrability in N =4 SYM
• Double Yangian and reflection algebras of the Lie superalgebra ${\mathfrak{gl}}_{m|n}$
• Supersymmetric $t$-$J$ models with long-range interactions: thermodynamics and criticality
• Super Yangian Double $DY(gl(1|1))$ and Its Gauss Decomposition