From Coalgebra to Bialgebra for the Six-Vertex Model: The Star-Triangle Relation as a Necessary Condition for Commuting Transfer Matrices

Axioms

关键词: vertex model;    bialgebra;    coalgebra;    Bethe ansatz;   

DOI  :  10.3390/axioms1020186

来源: mdpi

【 摘 要 】

Using the most elementary methods and considerations, the solution of the star-triangle condition is shown to be a necessary condition for the extension of the operator coalgebra of the six-vertex model to a bialgebra. A portion of the bialgebra acts as a spectrum-generating algebra for the algebraic Bethe ansatz, with which higher-dimensional representations of the bialgebra can be constructed. The star-triangle relation is proved to be necessary for the commutativity of the transfer matrices T(a, b, c) and T(a', b', c').

【 授权许可】

CC BY   
© 2012 by the authors; licensee MDPI, Basel, Switzerland.