Quantum Response at Finite Fields and Breakdown of Chern Numbers

TL;DR

This paper investigates the behavior of quantum Hall systems under electric fields, revealing that the response is analytic except at zero field and that Chern number breakdown signifies a discontinuous transition, challenging phase transition interpretations.

Contribution

It demonstrates the analyticity of the electric response in quantum Hall models and shows that Chern number breakdown in Floquet states is a discontinuous transition at zero field.

Findings

Response to electric field is analytic except at zero field.

Chern numbers for finite-dimensional Floquet operators are usually zero.

Breakdown of Chern numbers is a discontinuous transition at zero field.

Abstract

We show that the response to an electric field, in models of the Integral Quantum Hall effect, is analytic in the field and has isolated essential singularity at zero field. We also study the breakdown of Chern numbers associated with the response of Floquet states. We argue, and give evidence, that the breakdown of Chern numbers in Floquet states is a discontinuous transition at zero field. This follows from an observation, of independent interest, that Chern numbers for finite dimensional Floquet operators are generically zero. These results rule out the possibility that the breakdown of the Hall conductance is a phase transition at finite fields for a large class of models.