The Transfer Matrix of Superintegrable Chiral Potts Model as the Q-operator of Root-of-unity XXZ Chain with Cyclic Representation of Uq(sl2)
نویسنده
چکیده
We demonstrate that the transfer matrix of the inhomogeneous N -state chiral Potts model with two vertical superintegrable rapidities serves as the Q-operator of XXZ chain model for a cyclic representation of Uq(sl2) with Nth root-of-unity q and representation-parameter. The symmetry problem of XXZ chain with a general cyclic Uq(sl2)-representation is mapped onto the problem of studying Q-operator of some special one-parameter family of generalized τ models. In particular, the spin2 XXZ chain model with q N = 1 and the homogeneous N -state chiral Potts model at a specific superintegrable point are unified as one physical theory. By Baxter’s method developed for producing Q72-operator of the root-of-unity eight-vertex model, we construct the QR, QLand Q-operators of a superintegrable τ -model, then identify them with transfer matrices of the chiral Potts model. We thus obtain a new Q-operator method of producing the superintegrable N -state chiral Potts transfer matrix from the τ -model. 2006 PACS: 05.50.+q, 02.20.Uw, 75.10Jm 2000 MSC: 14H70, 39B72, 82B23
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