On a Network Model of Localization in a Random Magnetic Field

Abstract

We consider a network model of snake states to study the localization problem of non-interacting fermions in a random magnetic field with zero average. After averaging over the randomness, the network of snake states is mapped onto $M$ coupled SU$(2N)$ spin chains in the $N\to 0$ limit. The number of snake states near the zero-field contour, $M$, is an even integer. In the large conductance limit $g=M\frac{e^2}{2\pi \hslash }$ ($M\gg 2$), it turns out that this system is equivalent to a particular representation of the $\mathrm{U}(2N)/\mathrm{U}(N)\times \mathrm{U}(N)$ sigma model ($N\to 0$) {\it without} a topological term. The beta function $\beta (1/M)$ of this sigma model in the $1/M$ expansion is consistent with the previously known $\beta (g)$ of the unitary ensemble. These results and further plausible arguments support the conclusion that all the states are localized.

Revtex, 6 pages, 3 figures appended as an uuencoded file

References in corpus (6)

• A Unified Model for Two Localisation Problems: Electron States in Spin-Degenerate Landau Levels, and in a Random Magnetic Field
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• Self-duality of the integer quantum Hall to insulator transition: composite fermion description
• Random Magnetic Field and the Dirac Fermi Surface
• Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models
• Fermions in an anisotropic random magnetic field