2008/06/30 by Shi-shyr Roan
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #Quantum many-body systems #cond-mat.stat-mech #hep-th #math-ph #math.MP #math.QA #nlin.SI
paper · pdf · doi:10.1088/1751-8113/42/7/072003
published as J.Phys.A42:072003,2009 · Latex 11 pages; Typos corrected, Minor changes for clearer presentation, References added and updated-Journal version
openalex publication_date 2009/01/21 · arxiv created 2009/01/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We 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 a 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 cyclic representations with . The symmetry algebra of the τ (2) -model is described by the quantum affine algebra 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 2 N = 1 is equivalent to two copies of the same N -state τ (2) -model.