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 -