  Topological insulators are bulk electronic insulators which possess symmetry
protected gapless modes on their surfaces. Breaking the symmetries that
underlie the gapless nature of the surface modes is predicted to give rise to
exotic new states of matter. In particular, it has recently been predicted and
shown that breaking of time reversal symmetry in the form of ferromagnetism can
give rise to a gapped state characterized by a zero magnetic field quantized
Hall response and dissipationless longitudinal transport known as the Quantum
Anomalous Hall (QAH) state. A key question that has thus far remained
experimentally unexplored is the relationship of this new type of quantum Hall
state with the previously known orbitally driven quantum Hall states. Here, we
show experimentally that a ferromagnetic topological insulator exhibiting the
QAH state is well described by the global phase diagram of the quantum Hall
effect. By mapping the behavior of the conductivity tensor in the parameter
space of temperature, magnetic field, and chemical potential in the vicinity of
the QAH phase, we find evidence for quantum criticality and delocalization
behavior that can quantitatively be described by the renormalization group
properties of the quantum Hall ground state. This result demonstrates that the
QAH state observed in ferromagnetic topological insulators can be understood
within the context of the law of corresponding states which governs the quantum
Hall state. This suggests a roadmap for studying the QAH effect including
transitions to possible adjacent topologically non-trivial states and a
possible universality class for the QAH transition.

Strongly Correlated Electrons;Materials Science