Séminaire de Physique Théorique

The sl(2) loop algebra symmetry of the XXZ spin chain at roots of unity and the Ising-like spectrum of the superintegrable chiral Potts model
Tetsuo Deguchi (Ochanomizu University, Tokyo)
Tuesday 04 March 2008 14:00 -  Tours -  Salle 1180 (Bât E2)

Résumé :
We show the sl(2) loop algebra symmetry in some sectors of the spin-N/2 XXZ spin chain at roots of unity with q^N=1. Here the higher-spin XXZ chain is associated with the superintegrable chiral Potts model (SCP model). It was conjectured that each irreducible representation of the sl(2) loop algebra symmetry should correspond to an irreducible representation of the Onsager algebra for the SCP model (A. Nishino and T.D. Phys. Lett. A 356 (2006) pp. 366-370.) Here we also discuss another conjecture that the twisted transfer matrix of the six-vertex model at roots of unity with some discrete twist angles should have the sl(2) loop algebra symmetry (T. D., arXiv:0712.0066v1). Assuming the two conjectures, we discuss the Ising-like spectrum of the superintegrable chiral Potts model. We also review some recent relevant results. (This work is partially in collaboration with Akinori Nishino.)

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