Year: 2006
Type: article
Abstract: We compute the operator which creates the missing degenerate states in the algebraic Bethe ansatz of the eight-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 [12] 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 the transfer matrix T is enlarged to become { s , t , λ c ,1 , ..., λ c , n } with arbitrary string centres λ c , j and arbitrary n .
Authors: Klaus Fabricius, Barry M McCoy
Institutions: University of Wuppertal, Stony Brook University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2061293983