The TQ equation of the 8 vertex model for complex elliptic roots of unity

Abstract

We extend our studies of the TQ equation introduced by Baxter in his 1972 solution of the 8 vertex model with parameter $\eta$ given by $2L\eta =2m_{1}K+i{m}_2{K}^{\prime }$ from $m_2=0$ to the more general case of complex $\eta .$ We find that there are several different cases depending on the parity of $m_1$ and $m_2$.

arXiv comment30 pages, LATEX

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Cited by in corpus (9)

• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• The 8-vertex model with quasi-periodic boundary conditions
• Algebraic Bethe Ansatz approach to form factors and correlation functions of the cyclic eight-vertex solid-on-solid model
• New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity
• Q-operators for higher spin eight vertex models with an even number of sites
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• Q-operators for higher spin eight vertex models with a rational anisotropy parameter
• Properties of the String Operator in the Eight-Vertex Model