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Bethe ansatz equations for the broken Z$_{N}$-symmetric model

Yamada, Y

Published Jan 1, 1995• 1 citation
OpenAlex

Abstract

We obtain the Bethe Ansatz equations for the broken {\bf Z}_{N}-symmetric model by constructing a functional relation of the transfer matrix of L-operators. This model is an elliptic off-critical extension of the Fateev-Zamolodchikov model. We calculate the free energy of this model on the basis of the string hypothesis.

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Bethe ansatz equations for the broken ZN_{N}N​-symmetric model
A Bethe Ansatz study of a self dual ZN spin model is undertaken for even spin system. One has to solve a coupled system of Bethe Ansatz Equations (BAE) involving zeroes of two families of transfer matrices. A numerical study on finite size lattices is done for identification of elementary excitations over the Ferromagnetic and Antiferromagnetic ground states. The free energies for both Ferromagnetic and Antiferromagnetic ground states and dispersion relation for elementary excitations are found. I.
A Bethe–Ansatz study of a self-dual ZN spin model is undertaken for even spin system. One must solve a coupled system of Bethe–Ansatz equations (BAE) involving zeroes of two families of transfer matrices. A numerical study on finite size lattices is done for identification of elementary excitations over the ferromagnetic and antiferromagnetic ground states. The free energies for both ferromagnetic and antiferromagnetic ground states and dispersion relation for elementary excitations are found.
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 .