Exact edge current between boundaries of a strip of finite width

Employing an inhomogeneous solvable lattice model, we derive an exact expression for a boundary-to-boundary edge current on a lattice of finite width. This current is an example of a class of parafermionic observables recently introduced in an attempt to rigorously prove conformal invariance of the scaling limit of critical two-dimensional lattice models. It also corresponds to the classical limit of an edge current for the integer quantum Hall effect in the context of the Chalker-Coddington model. Our result is derived from a solution of the q-deformed Knizhnik-Zamolodchikov equation, and is expressed in terms of a symplectic Toda-lattice wave-function.