Exact spin quantum Hall current between boundaries of a lattice strip |
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Authors: | Jan de Gier Bernard Nienhuis Anita Ponsaing |
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Affiliation: | 1. Department of Mathematics and Statistics, The University of Melbourne, VIC 3010, Australia;2. Institute for Theoretical Physics, University of Amsterdam, The Netherlands |
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Abstract: | Employing an inhomogeneous solvable lattice model, we derive an exact expression for a boundary-to-boundary 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. |
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