The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism

Abstract

Based on the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the $k\times k$ fusion eight-vertex model in terms of the corresponding fusion SOS model. Here $k\in Z_{>0}$. A general formula for correlation functions is derived as a trace over the space of states of lattice operators such as the corner transfer matrices, the half transfer matrices (vertex operators) and the tail operator. We give a realization of these lattice operators as well as the space of states as objects in the level $k$ representation theory of the elliptic algebra $U_{q,p}({\widehat{sl}}_2)$.

arXiv comment54 pages, minor corrections to original version

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Cited by in corpus (17)

• Form factors of integrable Heisenberg (higher) spin chains
• Exact Form-Factor Results for the Longitudinal Structure Factor of the Massless XXZ Model in Zero Field
• Tracking the effects of interactions on spinons in gapless Heisenberg chains
• Correlation functions of the integrable higher-spin XXX and XXZ spin chains through the fusion method
• Elliptic Quantum Group U_{q,p}(\hat{sl}_2), Hopf Algebroid Structure and Elliptic Hypergeometric Series
• Dynamical R Matrices of Elliptic Quantum Groups and Connection Matrices for the q-KZ Equations
• Elliptic Quantum Group U_{q,p}(\hat{sl}_2) and Vertex Operators
• Quantum edge modes in 3d gravity and 2+1d topological phases of matter
• Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models
• Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model
• Theta function solutions of the qKZB equation for a face model
• Elliptic algebra, Frenkel-Kac construction and root of unity limit
• Vertex operator approach for form factors of Belavin's $(Z/nZ)$-symmetric model
• A Vertex Operator Approach for Form Factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-Symmetric Model and Its Application
• Form factors of spin 1 analogue of the eight-vertex model
• Boltzmann weights and fusion procedure for the rational seven-vertex SOS model
• Quantum Group U_q(sl(2)) Symmetry and Explicit Evaluation of the One-Point Functions of the Integrable Spin-1 XXZ Chain