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Employing an inhomogeneous solvable lattice model, we derive an exactexpression for a boundary-to-boundary edge current on a lattice of finitewidth. This current is an example of a class of parafermionic observablesrecently introduced in an attempt to rigorously prove conformal invariance ofthe scaling limit of critical two-dimensional lattice models. It alsocorresponds to the spin current at the spin-Quantum Hall transition in a modelintroduced by Chalker and Coddington, and generalized by Gruzberg, Ludwig andRead. Our result is derived from a solution of the $q$-deformedKnizhnik-Zamolodchikov equation, and is expressed in terms of a symplecticToda-lattice wave-function.

Exact spin quantum Hall current between boundaries of a lattice strip