Exact spin quantum Hall current between boundaries of a lattice strip

Abstract

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 spin current at the spin-Quantum Hall transition in a model introduced by Chalker and Coddington, and generalized by Gruzberg, Ludwig and Read. 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.

22 pages, 26 postscript figures, revised version

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• Type $\hat{\mathrm{C}}$ Brauer loop schemes and loop model with boundaries
• Currents in the dilute $O(n=1)$ model
• Finite size lattice results for the two-boundary Temperley--Lieb loop model
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