Global quantum Hall phase diagram from visibility diagrams

Abstract

Starting from a framework encoding rather simple symmetry principle based on modular subgroups, we construct a zero temperature global phase diagram for the QHE. This phase diagram is found to involve two insulating phases. One noticeable prediction is the possibility to have direct transitions from an insulting phase to any integer ν as well as ν=1/(2 k+1) ( k∈ N ) fractional quantum Hall liquid phases which seems to agree with some recent experimental observations. We also propose selection rules for the possible plateau–plateau (and plateau–insulator) transitions which may constitute testable predictions.