TY - JOUR

T1 - Eigenvectors in the superintegrable model II

T2 - Ground-state sector

AU - Au-Yang, Helen

AU - Perk, Jacques H.H.

PY - 2009

Y1 - 2009

N2 - In 1993, Baxter gave eigenvalues of the transfer matrix of the N-state superintegrable chiral Potts model with the spin-translation quantum number Q, where mQ = ⌊(NL - L - Q)/N⌋. 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 τ2 matrix has a degenerate eigenspace generated by the generators of r = m0 simple algebras. These results enable us to express the transfer matrix in the subspace in terms of these generators E1 m and Hm for m = 1, ..., r. Moreover, the corresponding 2r eigenvectors of the transfer matrix are expressed in terms of rotated eigenvectors of Hm.

AB - In 1993, Baxter gave eigenvalues of the transfer matrix of the N-state superintegrable chiral Potts model with the spin-translation quantum number Q, where mQ = ⌊(NL - L - Q)/N⌋. 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 τ2 matrix has a degenerate eigenspace generated by the generators of r = m0 simple algebras. These results enable us to express the transfer matrix in the subspace in terms of these generators E1 m and Hm for m = 1, ..., r. Moreover, the corresponding 2r eigenvectors of the transfer matrix are expressed in terms of rotated eigenvectors of Hm.

UR - http://www.scopus.com/inward/record.url?scp=70449585300&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/37/375208

DO - 10.1088/1751-8113/42/37/375208

M3 - Article

SN - 1751-8113

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 37

M1 - 375208

ER -