Eigenvectors of an Arbitrary Onsager Sector in Superintegrable $τ^{(2)}$-model and Chiral Potts Model

Details Eigenvectors of an Arbitrary Onsager Sector in Superintegrable $τ^{(2)}$-model and Chiral Potts Model Eigenvectors of an Arbitrary Onsager Sector in Superintegrable $τ^{(2)}$-model and Chiral Potts Model

2010-03-18

arxiv.org/abs/1003.3621v4

Physics

Mathematical Physics

Latex 43 Pages; Typos and errors corrected, Improved version with major modifications and extensions in Sections 3, 5 and 6. T

Scientific paper

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 $sl_2$-loop-algebra symmetry of the superintegrable $\tau^{(2)}$-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 $\tau^{(2)}$-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 $\tau^{(2)}$-model through its equivalent spin-$\frac{N-1}{2}$-XXZ chain. The $\tau^{(2)}$-eigenvectors in a sector are derived from the Bethe state and the $sl_2$-product structure determined by the Fabricius-McCoy current of the sector. From those $\tau^{(2)}$-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.

Affiliated with

Also associated with

No associations

Rating

Eigenvectors of an Arbitrary Onsager Sector in Superintegrable $τ^{(2)}$-model and Chiral Potts Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Eigenvectors of an Arbitrary Onsager Sector in Superintegrable $τ^{(2)}$-model and Chiral Potts Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Eigenvectors of an Arbitrary Onsager Sector in Superintegrable $τ^{(2)}$-model and Chiral Potts Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-700691