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Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit.

TitleDevil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit.
Publication TypeJournal Article
Year of Publication2016
AuthorsRotondo, P, Molinari, LGuido, Ratti, P, Gherardi, M
JournalPhys Rev Lett
Volume116
Issue25
Pagination256803
Date Published2016 Jun 24
ISSN1079-7114
Abstract

After more than three decades, the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we consider the so-called thin-torus limit of the Hamiltonian describing interacting electrons in a strong magnetic field, restricted to the lowest Landau level, and we show that it can be mapped onto a one-dimensional lattice gas with repulsive interactions, with the magnetic field playing the role of the chemical potential. The statistical mechanics of such models leads us to interpret the sequence of Hall plateaux as a fractal phase diagram whose landscape shows a qualitative agreement with experiments.

DOI10.1103/PhysRevLett.116.256803
Alternate JournalPhys. Rev. Lett.
PubMed ID27391740