Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-07-11
J.Phys.A40:1481-1512,2007
Physics
Condensed Matter
Statistical Mechanics
Latex 33 Pages; Typos and errors corrected, New improved version by adding explanations for better presentation. Terminology i
Scientific paper
10.1088/1751-8113/40/7/005
We construct the fusion operators in the generalized $\tau^{(2)}$-model using the fused $L$-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe ansatz discussion is conducted on two special classes of $\tau^{(2)}$ which include the superintegrable chiral Potts model. We then perform the parallel discussion on the XXZ spin chain at roots of unity, and demonstrate that the $sl_2$-loop-algebra symmetry exists for the root-of-unity XXZ spin chain with a higher spin, where the evaluation parameters for the symmetry algebra are identified by the explicit Fabricius-McCoy current for the Bethe states. Parallels are also drawn to the comparison with the superintegrable chiral Potts model.
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