Eigenvectors in the Superintegrable Model II: Ground State Sector

Details Eigenvectors in the Superintegrable Model II: Ground State Sector Eigenvectors in the Superintegrable Model II: Ground State Sector

2008-03-20

arxiv.org/abs/0803.3029v4

J. Phys. A: Math. Theor. 42 (2009) 375208

Physics

Mathematical Physics

LaTeX 2E document, using iopart.cls with iopams packages. 17 pages, uses eufb10 and eurm10 fonts. Typeset twice! vs2: Many cha

Scientific paper

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 $H_m$.

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