Crystallizing the spinon basis

1995/04/10 by Atsushi Nakayashiki, Yasuhiko Yamada
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Basis (linear algebra) #Black Holes and Theoretical Physics #Character (mathematics) #Geometry #Integrable system #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #Spin (aerodynamics) #Spinon #Thermodynamics #Yangian #hep-th

paper · pdf · doi:10.1007/bf02104914

published as Commun. Math. Phys. 178 (1996) 179 · 25 pages, latex

arxiv created 1995/04/10 · openalex publication_date 1996/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The quasi-particle structure of the higher spin XXZ model is studied. We obtained a new description of crystals associated with the level k integrable highest weight U_q(\widehatsl₂) modules in terms of the creation operators at q=0 (the crystaline spinon basis). The fermionic character formulas and the Yangian structure of those integrable modules naturally follow from this description. We have also derived the conjectural formulas for the multi quasi-particle states at q=0.

Citations

• On crystal bases of the Q-analogue of universal enveloping algebras
• Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory
• Dilogarithm Identities