Abstract
The twenty-one-vertex model, the spin $1$ analogue of the eight-vertex model is considered on the basis of free field representations of vertex operators in the $2\times 2$-fold fusion SOS model and vertex-face transformation. The tail operators, which translate corner transfer matrices of the twenty-one-vertex model into those of the fusion SOS model, are constructed by using free bosons and fermions for both diagonal and off-diagonal matrix elements with respect to the ground state sectors. Form factors of any local operators are therefore obtained in terms of multiple integral formulae, in principle. As the simplest example, the two-particle form factor of the spin operator is calculated explicitly.
Highlights
In this paper we consider the spin 1 analogue of Baxter’s eight-vertex model [1], on the basis of vertex operator approach [2]
Lashkevich and Pugai [3] found that the correlation functions of the eight-vertex model can be obtained by using the free field realization of the vertex operators in the eight-vertex SOS model [4], with insertion of the nonlocal operator Λ, called ‘the tail operator’
Correlation functions in the twenty-one-vertex model can be constructed in terms of type I vertex operators of fusion SOS model and tail operators as follows: 1 χ(i)
Summary
In this paper we consider the spin 1 analogue of Baxter’s eight-vertex model [1], on the basis of vertex operator approach [2]. The vertex operator approach for higher spin generalization of the eight-vertex model was presented in [6]. Spin 1 analogue of the eight-vertex model (twenty-one-vertex model) can be described in terms of one boson and one fermion, because c. Konno and Weston [6] constructed vertex operator formalism for the higher spin analogue of the eight-vertex model, by using vertex-face transformation onto k × k fusion SOS model. In Appendix C, the details of derivation are given for the free filed representations of the tail operators off-diagonal with respect to the ground state sectors
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