Chiral Potts model as a discrete quantum sine-Gordon model

Helen Au-Yang Eigenvectors of the superintegrable chiral Potts model We show that the eigenspaces of eigenvalues (1−ωt)+ω(1− t) of the τ2(t) matrix of size N×N are degenerate. In the Q = 0 case, it has 2 independent eigenvectors, where r = L(N − 1)/N and L is chosen to be a multiple of N . They can be written in terms of the generators of r simple sl2 algebras, E±m and Hm (m = 1, · · · , r). Next we use a result of Baxter on the correponding 2 eigenvalues of the transfer matrix of the N-state superintegrable chiral Potts model and show that in this sector the transfer matrix can also be expressed in terms of these generators. Finally, the corresponding 2 eigenvectors are given in terms of rotated eigenvectors of Hm.