Quantum affine symmetry in vertex models

Abstract

We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin $1/2$, and that the $n$-particle space has an RSOS-type structure rather than a simple tensor product of the $1$-particle space. This agrees with the picture proposed earlier by Reshetikhin.

29 pages

References in corpus (2)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Diagonalization of the XXZ Hamiltonian by Vertex Operators

Cited by in corpus (39)

• The half-infinite XXZ chain in Onsager's approach
• Hirota equation as an example of integrable symplectic map
• The Yangian symmetry of the Hubbard Model
• Spinons in Magnetic Chains of Arbitrary Spins at Finite Temperatures
• Vertex operators in solvable lattice models
• Reduced qKZ equation and correlation functions of the XXZ model
• Staggered Polarization of Vertex Models with $U_q(\widehat{sl}(n))$-Symmetry
• Free Boson Realization of $U_q(\widehat{s{l}_N})$
• Free Boson Representation of $q$-Vertex Operators and their Correlation Functions
• Crystalizing the Spinon Basis
• A Q-Operator Identity for the Correlation Functions of the Infinite XXZ Spin-Chain
• The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism
• N-point Correlation Functions of the Spin-1 XXZ Model
• The Entanglement Entropy of Solvable Lattice Models
• Non-Abelian symmetries of the half-infinite XXZ spin chain
• Free Field Representation of Quantum Affine Algebra $U_q\widehat{s{l}_2}$ and Form Factors in Higher Spin XXZ Model
• Crystalline Spinon Basis for RSOS Models
• Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
• Difference equations with elliptic coefficients and quantum affine algebras
• Mixing of Ground States in Vertex Models
• Fusion of the $q$-Vertex Operators and its Application to Solvable Vertex Models
• Vertex Models with Alternating Spins
• Cladistics of Double Yangians and Elliptic Algebras
• Density matrices in integrable face models
• Quantum R-matrix and Intertwiners for the Kashiwara Algebra
• Free Boson Representation of $U_q({\widehat{sl}}_3)$
• Solutions to the Quantized Knizhnik-Zamolodchikov Equation and the Bethe Ansatz
• On the Bosonization of $L$-Operators for Quantum Affine Algebra $U_q(s{l}_2)$
• Free Field Approach to Solutions of the Quantum Knizhnik-Zamolodchikov Equations
• Quiver varieties and quantum Knizhnik--Zamolodchikov equation
• N-point matrix elements of dynamical vertex operators of the higher spin XXZ model
• Crystallized structure for level 0 part of modified quantum affine algebra
• Path representation of su(2)_k states II: Operator construction of the fermionic character and spin-1/2--RSOS factorization
• Higher spin polynomial solutions of quantum Knizhnik--Zamolodchikov equation
• A $U_q(\widehat{gl}(2|2){)}_1$-Vertex Model: Creation Algebras and Quasi-Particles I
• Dynamical supersymmetry on the XXX spin chain
• q-Wakimoto Modules and Integral Formulae of the Quantum Knizhnik-Zamolodchikov Equations
• Spontaneous polarization of the Kondo problem associated with the higher-spin six-vertex model
• Impurity Operators in RSOS Models