- 99-155 J. E. Avron and Z. Kons
- Quantum Response at Finite Fields and Breakdown of Chern Numbers
(173K, Latex2e and 7 eps figure files)
May 9, 99
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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
{\em 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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