Quantum Hall criticality in Floquet topological insulators

TL;DR

This paper demonstrates that the topological phase transition in the anomalous Floquet Anderson insulator (AFAI) shares the same universality class as the integer quantum Hall effect, despite differences in physical mechanisms.

Contribution

It establishes a theoretical mapping of AFAI to IQH universality class and derives an effective theory based on symmetry and topological criteria, confirmed by numerical tests.

Findings

AFAI phase transition is in the IQH universality class.

Effective theory matches Pruisken's IQH theory.

Numerical simulations confirm predictions about transport and delocalization.

Abstract

The anomalous Floquet Anderson insulator (AFAI) is a two dimensional periodically driven system in which static disorder stabilizes two topologically distinct phases in the thermodynamic limit. The presence of a unit-conducting chiral edge mode and the essential role of disorder induced localization are reminiscent of the integer quantum Hall (IQH) effect. At the same time, chirality in the AFAI is introduced via an orchestrated driving protocol, there is no magnetic field, no energy conservation, and no (Landau level) band structure. In this paper we show that in spite of these differences the AFAI topological phase transition is in the IQH universality class. We do so by mapping the system onto an effective theory describing phase coherent transport in the system at large length scales. Unlike with other disordered systems, the form of this theory is almost fully determined by symmetry and topological consistency criteria, and can even be guessed without calculation. (However, we back this expectation by a first principle derivation.) Its equivalence to the Pruisken theory of the IQH demonstrates the above equivalence. At the same time it makes predictions on the emergent quantization of transport coefficients, and the delocalization of bulk states at quantum criticality which we test against numerical simulations.