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 a chemical potential. The statistical mechanics of such models leads to interpret the sequence of Hall plateaux as a fractal phase diagram, whose landscape shows a qualitative agreement with experiments.

5 pages main text, 11 pages supplementary, 2 figures

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• Statistical learning theory of structured data
• Devil's staircases in synthetic dimensions and gauge fields
• Bosonic integer quantum Hall effect as topological pumping
• Self-induced glassy phase in multimodal cavity quantum electrodynamics
• Generalized Devil's staircase and RG flows
• Unified Fock space representation of fractional quantum Hall states
• Emergent Mott-insulators at non-integer fillings and devil's staircase induced by attractive interaction in many-body polarons
• Quantum frustrated Wigner chains
• Fractal ground state of ion chains in periodic potentials
• Current quantization and fractal hierarchy in a driven repulsive lattice gas
• Jack on a Devil's staircase
• Excitation and tunneling spectra of a fractional quantum Hall system in the thin cylinder limit