Vertex operators in solvable lattice models

Abstract

We formulate the basic properties of q-vertex operators in the context of the Andrews-Baxter-Forrester (ABF) series, as an example of face-interaction models, derive the q-difference equations satisfied by their correlation functions, and establish their connection with representation theory. We also discuss the q-difference equations of the Kashiwara-Miwa (KM) series, as an example of edge-interaction models. Next, the Ising model--the simplest special case of both ABF and KM series--is studied in more detail using the Jordan-Wigner fermions. In particular, all matrix elements of vertex operators are calculated.

41 pages

References in corpus (5)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Diagonalization of the XXZ Hamiltonian by Vertex Operators
• Quantum affine symmetry in vertex models
• Difference equations for the correlation functions of the eight vertex model
• Structure of the space of states in RSOS models

Cited by in corpus (36)

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• Determinant Representations for Correlation Functions of Spin-1/2 XXX and XXZ Heisenberg Magnets
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• Free Field Construction for Correlation Functions of the Eight-Vertex Model
• Bosonization of ZF Algebras: Direction Toward Deformed Virasoro Algebra
• Lukyanov's Screening Operators for the Deformed Virasoro Algebra
• The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism
• Free Field Construction for the ABF Models in Regime II
• Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem
• Quantum Black hole--White hole entangled states
• Free Field Approach to the Dilute A_L Models
• Correlation functions for the Z-invariant Ising model
• Virasoro-type Symmetries in Solvable Models
• Free field constructions for the elliptic algebra ${\mathcal{A}}_{q,p}({\widehat{sl}}_2)$ and Baxter's eight-vertex model
• A unified treatment of Ising model magnetizations
• Vertex Models with Alternating Spins
• Type II vertex operators for the $A_{n-1}^{(1)}$ face model
• Fusion of the $q$-Vertex Operators and its Application to Solvable Vertex Models
• Nearest neighbor two-point correlation function of the $Z$-invariant eight-vertex model
• Elliptic Deformed Superalgebra $u_{q,p}(\widehat{sl}(M|N))$
• On the Hydrogen Atom in the Holographic Universe
• Factorization of density matrices in the critical RSOS models
• Density matrices in integrable face models
• Bootstrap equations and correlation functions for the Heisenberg XYZ antiferromagnet
• Quasi-Hopf twist and elliptic Nekrasov factor
• A Quantum Analogue of the $\mathcal{Z}$ Algebra
• Infinite dimensional symmetry of corner transfer matrices
• The elliptic quantum algebra $A_{q,p}(\widehat{s{l}_n})$ and its bosonization at level one
• Difference equations for correlation functions of $A_{n-1}^{(1)}$-face model with boundary reflection
• Free Field Realization of Vertex Operators for Level Two Modules of $U_q(\widehat{sl(2)})$
• Theta function solutions of the qKZB equation for a face model
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• Lattice models, deformed Virasoro algebra and reduction equation
• Impurity Operators in RSOS Models
• Spontaneous polarization of the Kondo problem associated with the higher-spin six-vertex model