Crystalizing the Spinon Basis

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 $U_q(\widehat{s{l}_2})$ 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 $q=0$.

25 pages, latex

References in corpus (8)

• Dilogarithm identities
• Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
• Quantum affine symmetry in vertex models
• Spinons in Conformal Field Theory
• Characters in Conformal Field Theories from Thermodynamic Bethe Ansatz
• Spinon basis for higher level SU(2) WZW models
• The sums of Rogers, Schur and Ramanujan and the Bose-Fermi correspondence in $1+1$-dimensional quantum field theory
• Structure of the space of states in RSOS models

Cited by in corpus (23)

• Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
• Exclusion Statistics in Conformal Field Theory -- generalized fermions and spinons for level-1 WZW theories
• The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
• Fermionic solution of the Andrews-Baxter-Forrester model II: proof of Melzer's polynomial identities
• Polynomial Identities, Indices, and Duality for the N=1 Superconformal Model SM(2,4ν)
• Non-abelian Exclusion Statistics
• A Matrix Model for WZW
• Crystalline Spinon Basis for RSOS Models
• Conjugate Bailey pairs
• Level-0 structure of level-1 $U_q({\widehat{sl}}_2)$-modules and Macdonald polynomials
• Exclusion statistics in conformal field theory and the UCPF for WZW models
• Spectral Decomposition of Path Space in Solvable Lattice Model
• Kostka Polynomials and Energy Functions in Solvable Lattice Models
• Characters for ${\widehat{sl(n)}}_{k=1}$ from a novel Thermodynamic Bethe Ansatz
• Symmetry protected topological phases beyond groups: The q-deformed bilinear-biquadratic spin chain
• Fusion of the $q$-Vertex Operators and its Application to Solvable Vertex Models
• Vertex Models with Alternating Spins
• Higher string functions, higher-level Appell functions, and the logarithmic ^sl(2)_k/u(1) CFT model
• Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry
• On $q$-Clebsch Gordan Rules and the Spinon Character Formulas for Affine $C_2^{(1)}$ Algebra
• Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization
• A $U_q(\widehat{gl}(2|2){)}_1$-Vertex Model: Creation Algebras and Quasi-Particles I
• Path representation of su(2)_k states I: Operators and particles for k=1,2