Luca Molinari — Università di Milano #
Devil's Staircase Phase Diagram of the Fractional Quantum Hall Effect in the Thin-Torus Limit#
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. We show that, in the thin-torus limit,
the Hamiltonian for interacting electrons in a strong magnetic field, restricted to the lowest Landau level,
can be mapped onto a 1D lattice gas with repulsive interactions, with the magnetic field
playing the role of the 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.