Exact spin quantum Hall current between boundaries of a lattice strip

TL;DR

This paper derives an exact boundary-to-boundary edge current in a finite lattice model, connecting quantum Hall physics with parafermionic observables and conformal invariance, using advanced algebraic methods.

Contribution

It provides a novel exact expression for a boundary current in a solvable lattice model, linking quantum Hall effects with parafermionic observables and integrable systems.

Findings

Exact boundary-to-boundary current expression derived

Connects quantum Hall spin current with parafermionic observables

Uses q-deformed KZ equation and symplectic Toda wave-function

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.