An elliptic current operator for the 8 vertex model

Details An elliptic current operator for the 8 vertex model An elliptic current operator for the 8 vertex model

2006-06-07

arxiv.org/abs/cond-mat/0606190v4

J.Phys. A39 (2006) 14869-14886

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/0305-4470/39/48/003

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,\lambda_{c,1}, ..., \lambda_{c,n}\} with arbitrary string centers \lambda_{c,j} and arbitrary n.

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