An elliptic current operator for the 8 vertex model

Abstract

We compute the operator which creates the missing degenerate states in the algebraic Bethe ansatz of the 8 vertex model at roots of unity and relate it to the concept of an elliptic current operator. We find that in sharp contrast with the corresponding formalism in the six-vertex model at roots of unity the current operator is not nilpotent with the consequence that in the construction of degenerate eigenstates of the transfer matrix an arbitrary number of exact strings can be added to the set of regular Bethe roots. Thus the original set of free parameters {s,t} of an eigenvector of T is enlarged to become {s,t,λ_{c,1}, ..., λ_{c,n}\} with arbitrary string centers λ_{c,j} and arbitrary n.

16 pages, Latex typographic errors corrected, text added, reference added, accepted by Journal of Physics A,Mathematical and General

References in corpus (7)

• Algebraic Bethe ansatz for the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• On representations of the elliptic quantum group $E_{\tau ,\eta }(s{l}_2)$
• Bethe's equation is incomplete for the XXZ model at roots of unity
• Cyclic monodromy matrices for sl(n) trigonometric R-matrices
• Construction of some missing eigenvectors of the XYZ spin chain at the discrete coupling constants and the exponentially large spectral degeneracy of the transfer matrix
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• The 8V CSOS model and the $s{l}_2$ loop algebra symmetry of the six-vertex model at roots of unity

Cited by in corpus (7)

• The Baxter's Q-operator for the W-algebra $W_N$
• Analytic theory of the eight-vertex model
• XXZ Bethe states as highest weight vectors of the $s{l}_2$ loop algebra at roots of unity
• The eight-vertex model and lattice supersymmetry
• The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity $\eta =\frac{2mK}{N}$ for odd N
• A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain
• Properties of the String Operator in the Eight-Vertex Model