title: Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit.
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.
authors.affiliation: Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy.|INFN Milano, via Celoria 16, 20133 Milano, Italy.
authors.forename: Pietro
authors.initials: P
authors.lastname: Rotondo
authors.affiliation: Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy.|INFN Milano, via Celoria 16, 20133 Milano, Italy.
authors.forename: Luca Guido
authors.initials: LG
authors.lastname: Molinari
authors.affiliation: Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy.
authors.forename: Piergiorgio
authors.initials: P
authors.lastname: Ratti
authors.affiliation: Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy.|Sorbonne Universités, UPMC Université Paris 06, UMR 7238, Computational and Quantitative Biology, 15 rue de l'École de Médecine, 75006 Paris, France.
authors.forename: Marco
authors.initials: M
authors.lastname: Gherardi