Quantum Response at Finite Fields and Breakdown of Chern Numbers

Details Quantum Response at Finite Fields and Breakdown of Chern Numbers Quantum Response at Finite Fields and Breakdown of Chern Numbers

1999-01-23

arxiv.org/abs/math-ph/9901018v2

J.Phys.A32:6097-6113,1999

Physics

Mathematical Physics

16 pages, 8 eps figures, LaTeX2e with IOP style. Many changes, including new material

Scientific paper

10.1088/0305-4470/32/33/308

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.

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