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 $s{l}_2$ 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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References in corpus (5)

• The L(sl_2) symmetry of the Bazhanov-Stroganov model associated with the superintegrable chiral Potts model
• XXZ Bethe states as highest weight vectors of the $s{l}_2$ loop algebra at roots of unity
• An algebraic derivation of the eigenspaces associated with an Ising-like spectrum of the superintegrable chiral Potts model
• Eigenvectors in the Superintegrable Model I: sl_2 Generators
• Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations

Cited by in corpus (13)

• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Parafermions in the tau-2 model
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• The tau_2-model and the chiral Potts model revisited: completeness of Bethe equations from Sklyanin's SOV method
• Spontaneous magnetization of the superintegrable chiral Potts model: calculation of the determinant D_PQ
• Identities in the Superintegrable Chiral Potts Model
• Spin operator matrix elements in the superintegrable chiral Potts quantum chain
• A conjecture for the superintegrable chiral Potts model
• Some ground-state expectation values for the free parafermion Z(N) spin chain
• Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices
• Spontaneous Magnetization of the Integrable Chiral Potts Model
• Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths