On the Form Factors of Local Operators in the Bazhanov–Stroganov and Chiral Potts Models

Abstract

We consider general cyclic representations of the six-vertex Yang–Baxter algebra and analyze the associated quantum integrable systems, the Bazhanov–Stroganov model and the corresponding chiral Potts model on finite size lattices. We first determine the propagator operator in terms of the chiral Potts transfer matrices and we compute the scalar product of separate states (including the transfer matrix eigenstates) as a single determinant formulae in the framework of Sklyanin’s quantum separation of variables. Then, we solve the quantum inverse problem and reconstruct the local operators in terms of the separate variables. We also determine a basis of operators whose form factors are characterized by a single determinant formulae. This implies that the form factors of any local operator are expressed as finite sums of determinants. Among these form factors written in determinant form are in particular those which will reproduce the chiral Potts order parameters in the thermodynamic limit. The results presented here are the generalization to the present models associated to the most general cyclic representations of the six-vertex Yang–Baxter algebra of those we derived for the lattice sine–Gordon model.