Eigenvectors in the Superintegrable Model II: Ground State Sector

Abstract

In 1993, Baxter gave $2^{m_Q}$ eigenvalues of the transfer matrix of the $N$-state superintegrable chiral Potts model with spin-translation quantum number $Q$, where $m_Q=\lfloor(NL-L-Q)/N\rfloor$. In our previous paper we studied the Q=0 ground state sector, when the size $L$ of the transfer matrix is chosen to be a multiple of $N$. It was shown that the corresponding $\tau_2$ matrix has a degenerate eigenspace generated by the generators of $r=m_0$ simple $sl_2$ algebras. These results enable us to express the transfer matrix in the subspace in terms of these generators $E_m^{\pm}$ and $H_m$ for $m=1,...,r$. Moreover, the corresponding $2^r$ eigenvectors of the transfer matrix are expressed in terms of rotated eigenvectors of $H_m$.