Journal article

Exact spin quantum Hall current between boundaries of a lattice strip

Jan de Gier, Bernard Nienhuis, Anita Ponsaing



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. © 2010 Elsevier B..

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University of Melbourne Researchers


Funding Acknowledgements

It is a pleasure to thank Luigi Cantini and Omar Foda for discussions about the Toda lattice. J.d.G. and A.P. would like to thank the Australian Research Council for financial support, and A.P. would like to thank the hospitality of the Henri Poincare Institute in Paris and The Rudolf Peierls Institute for Theoretical Physics in Oxford where part of this work was completed. B.N. is grateful for numerous scientific discussions with Jesper Jacobsen and Philippe Di Francesco that were instrumental to the conception of this paper. He also wishes to acknowledge the hospitality and financial support provided by the ARC Centre of Excellence MASCOS and the Department of Mathematics and Statistics at the University of Melbourne, as well as the financial support from the organisation FOM (which is part of NWO).