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Supersymmetry approach to delocalization transitions in a network model of the weak-field quantum Hall effect and related models

TitleSupersymmetry approach to delocalization transitions in a network model of the weak-field quantum Hall effect and related models
Publication TypeJournal Article
Year of Publication2014
AuthorsBhardwaj, S, Mkhitaryan, VV, Gruzberg, IA
JournalPhysical Review B
Volume89
Pagination235305
Date Published06
Type of ArticleArticle
ISBN Number1098-0121
Accession NumberWOS:000339621500004
Keywords2 dimensions, 2-dimensional electron-gas, anderson, bond alternation, insulator-transition, localization, phase-diagram, sigma-model, spin ladders, strong magnetic-field, symmetry classes
Abstract

We consider a recently proposed network model of the integer quantum Hall (IQH) effect in a weak magnetic field. Using a supersymmetry approach, we reformulate the network model in terms of a superspin ladder. A subsequent analysis of the superspin ladder and the corresponding supersymmetric nonlinear sigma model allows us to establish the phase diagram of the network model, and the form of the critical line of the weak-field IQH transition. Our results confirm the universality of the IQH transition, which is described by the same sigma model in strong and weak magnetic fields. We apply the suspersymmetry method to several related network models that were introduced in the literature to describe the quantum Hall effect in graphene, the spin-degenerate Landau levels, and localization of electrons in a random magnetic field.

DOI10.1103/PhysRevB.89.235305
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Nanoscale and Ultrafast