On $τ^{(2)}$-model in Chiral Potts Model and Cyclic Representation of Quantum Group $U_q(sl_2)$

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dc.creatorRoan, Shi-shyr
dc.date2008-06-02
dc.date2009-01-22
dc.date.accessioned2026-07-07T12:35:20Z
dc.date.available2026-07-07T12:35:20Z
dc.descriptionWe identify the precise relationship between the five-parameter $τ^{(2)}$-family in the $N$-state chiral Potts model and XXZ chains with $U_q (sl_2)$-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover an one-parameter family of $L$-operators in terms of the quantum group $U_q (sl_2)$. When $N$ is odd, the $N$-state $τ^{(2)}$-model can be regarded as the XXZ chain of $U_{\sf q} (sl_2)$ cyclic representations with ${\sf q}^N=1$. The symmetry algebra of the $τ^{(2)}$-model is described by the quantum affine algebra $U_{\sf q} (\hat{sl}_2)$ via the canonical representation. In general for an arbitrary $N$, we show that the XXZ chain with a $U_q (sl_2)$-cyclic representation for $q^{2N}=1$ is equivalent to two copies of the same $N$-state $τ^{(2)}$-model.
dc.descriptionLatex 11 pages; Typos corrected, Minor changes for clearer presentation, References added and updated-Journal version
dc.identifierhttps://arxiv.org/abs/0806.0216
dc.identifierhttp://arxiv.org/abs/0806.0216
dc.identifierJ.Phys.A42:072003,2009
dc.identifierdoi:10.1088/1751-8113/42/7/072003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217736
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.subjectExactly Solvable and Integrable Systems
dc.titleOn $τ^{(2)}$-model in Chiral Potts Model and Cyclic Representation of Quantum Group $U_q(sl_2)$
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