New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity

Abstract

The Q matrix invented by Baxter in 1972 to solve the eight vertex model at roots of unity exists for all values of N, the number of sites in the chain, but only for a subset of roots of unity. We show in this paper that a new Q matrix, which has recently been introduced and is non zero only for N even, exists for all roots of unity. In addition we consider the relations between all of the known Q matrices of the eight vertex model and conjecture functional equations for them.

20 pages, 2 Postscript figures

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Cited by in corpus (6)

• 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
• A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain
• Q-operators for higher spin eight vertex models with a rational anisotropy parameter
• Properties of the String Operator in the Eight-Vertex Model