Excitation spectrum of the anisotropic generalization of an SU3 magnet
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The method proposed for calculating the eigenvalues of the transfer matrix is based on some fundamental properties of the R matrix such as unitarity, cross symmetry, and special relations related to the structure of the degeneracy of the R matrix at certain points. One can therefore hope that it applies to a large class of models in which the complicated structure of the R matrix makes it impossible to construct n-particle eigenstates of the transfer matrix by the Bethe ansatz.
The specific example of the Izergin-Korepin model demonstrates that in the thermodynamic limit the cross symmetry and unitarity (64) and (65) are insufficient for the calculation of the eigenvalues of the transfer matrix by the “inverse transfer matrix” method. For unique determination of the positions of the singularities of the analytic continuation of Λ (λ) it is necessary to use the bootstrap relation (66). This also applies to some other models, in particular to systems with the R matrices found in [14, 15]. It has not been our intention to give a mathematically rigorous justification of the proposed method, which we defer to a separate publication.
KeywordsLarge Class Excitation Spectrum Analytic Continuation Transfer Matrix Special Relation
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