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Sfb288 logo Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 571


Fractional quantum Hall systems from Toda theories

O.A. Castro-Alvaredo, A. Fring

We analyse the expression for the conductance of a quantum wire which is decribed by an integrable quantum field theory. In the high temperature regime we derive a simple formula for the filling fraction. This expression involves only the inverse of a matrix which contains the information of the asymptotic phases of the scattering matrix and the solutions of the constant thermodynamic Bethe ansatz equations. Evaluating these expressions for minimal affine Toda field theory we recover several subsequences of the famous Jain sequence for the filling fraction occurring in the context of the fractional quantum Hall effect. For instance we obtain $ u= m/(2m +1)$ for $A_{4m-1}$-minimal affine Toda field theory. The matrices involved have in general non-rational entries and are not part of previous classification schemes based on integral lattices.


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