2010/03/18 by Shi-shyr Roan, Roan, Shi-shyr · 1 citation
Physics and Astronomy · Mathematics · #Quantum Mechanics and Non-Hermitian Physics #Algebraic structures and combinatorial models #Quantum and electron transport phenomena
paper · pdf · doi:10.48550/arxiv.1003.3621
We study the eigenvector problem in homogeneous superintegrable N-state chiral Potts model (CPM) by the symmetry principal. Using duality symmetry and (spin-)inversion in CPM, together with Onsager-algebra symmetry and sl2-loop-algebra symmetry of the superintegrable τ(2)-model, we construct the complete k'-dependent CPM-eigenvectors in the local spin basis for an arbitrary Onsager sector. In this paper, we present the complete classification of quantum numbers of superintegrable τ(2)-model. Accordingly, there are four types of sectors. The relationships among Onsager sectors under duality and inversion, together with their Bethe roots and CPM-eigenvectors, are explicitly found. Using algebraic-Bethe-ansatz techniques and duality of CPM, we construct the Bethe states and the Fabricius-McCoy currents of the superintegrable τ(2)-model through its equivalent spin-(N-1)/(2)-XXZ chain. The τ(2)-eigenvectors in a sector are derived from the Bethe state and the sl2-product structure determined by the Fabricius-McCoy current of the sector. From those τ(2)-eigenvectors, the k'-dependence of CPM state vectors in local-spin-basis form is obtained by the Onsager-algebra symmetry of the superintegrable chiral Potts quantum chain.