Exact spin quantum Hall current between boundaries of a lattice strip

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 scali...

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Bibliographic Details
Published inNuclear physics. B Vol. 838; no. 3; pp. 371 - 390
Main Authors de Gier, Jan, Nienhuis, Bernard, Ponsaing, Anita
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.10.2010
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Summary: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.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2010.05.019