Irreducible monodromy matrices for the R matrix of the XXZ model and local quantum lattice Hamiltonians

V. Tarasov

V. Tarasov

Irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model are described. As a consequence, the direct computation of spectra for transfer-matrices of the chiral Potts model with special fixed-spin boundary conditions is done. The generalization of simple Baxter's Hamiltonian is proposed.

V. Tarasov

V. Tarasov, Leon Armenovich Takhtadzhyan, L. D. Faddeev

Stephen Gerard McAteer, M. Wheeler

Using notation inherited from the six-vertex model, we construct diagrams that represent the action of the factorizing F-matrices associated to the finite length XXZ spin-12 chain. We provide a diagrammatic proof that these F-matrices factorize the tensor R1…nσ corresponding with elements of the permutation group. We consider in particular the diagram for the tensor R1…nσc, which cyclically permutes the spin chain. This leads us to a diagrammatic construction of the local spin operators Si± and Siz in terms of the monodromy matrix operators.

V. Tarasov, Leon Armenovich Takhtadzhyan, L. D. Faddeev