Free Field Construction for Correlation Functions of the Eight-Vertex Model

Abstract

A free field representation for the type $I$ vertex operators and the corner transfer matrices of the eight-vertex model is proposed. The construction uses the vertex-face correspondence, which makes it possible to express correlation functions of the eight-vertex model in terms of correlation functions of the SOS model with a nonlocal insertion. This new nonlocal insertion admits of a free field representation in terms of Lukyanov's screening operator. The spectrum of the corner transfer matrix and the Baxter--Kelland formula for the average staggered polarization have been reproduced.

22 pages, uses pictex.tex, typos corrected and minor changes

References in corpus (2)

• Algebra of screening operators for the deformed $W_n$ algebra
• Bosonization of vertex operators for Zn symmetric Belavin model and its correlation functions

Cited by in corpus (28)

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• The Vertex-Face Correspondence and Correlation Functions of the Fusion Eight-Vertex Model I: The General Formalism
• The 8-vertex model with quasi-periodic boundary conditions
• Exact and simple results for the XYZ and strongly interacting fermion 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
• Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
• Scalar products of Bethe vectors in the 8-vertex model
• On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain
• Correlation functions by Separation of Variables: the XXX spin chain
• The massless XXZ chain with a boundary
• Current mean values in the XYZ model
• Nearest neighbor two-point correlation function of the $Z$-invariant eight-vertex model
• Bootstrap equations and correlation functions for the Heisenberg XYZ antiferromagnet
• The Vertex-Face Correspondence and the Elliptic 6j-symbols
• Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models
• The critical $A_{n-1}^{(1)}$ chain
• Correlation functions of the XYZ model with a boundary
• Difference equations for correlation functions of $A_{n-1}^{(1)}$-face model with boundary reflection
• Vertex operator approach for form factors of Belavin's $(Z/nZ)$-symmetric model
• Vertex operator approach for correlation functions of Belavin's (Z/nZ)-symmetric model
• Difference equations for correlation functions of Belavin's $Z_n$-symmetric model with boundary reflection
• A Vertex Operator Approach for Form Factors of Belavin's $(\mathbb{Z}/n\mathbb{Z})$-Symmetric Model and Its Application
• Spontaneous polarization of the Kondo problem associated with the higher-spin six-vertex model
• Form factors of spin 1 analogue of the eight-vertex model