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Power-law corrections to the Kubo formula vanish in quantum Hall systems

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Abstract

In first order perturbation theory conductivity is given by the Kubo formula, which in a Quantum Hall System equals the first Chern class of a vector bundle. We apply the adiabatic theorem to show that these topological constraints quantize the averaged conductivity to all orders of perturbation theory. Hence the Kubo formula is valid to all orders.

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References

  • [AS] Avron, J.E., Seiler, R.: Quantisation of the Hall conductance for general multiparticle Schrödinger Hamiltonians. Phys. Rev. Lett.54, 259–262 (1985)

    Google Scholar 

  • [ASS] Avron, J.E., Seiler, R., Shapiro, B.: Generic properties of quantum Hall Hamiltonians for finite systems. Nucl. Phys.B 265, 364–374 (1986)

    Google Scholar 

  • [ASY] Avron, J.E., Seiler, R., Yaffe, L.G.: Adiabatic theorems and applications to the quantum Hall effect. Commun. Math. Phys.110, 33–49 (1987)

    Google Scholar 

  • [K1] Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1984

    Google Scholar 

  • [K2] Kato, T.: On the adiabatic theorem of quantum mechanics. J. Phys. Soc. J. Jpn.5, 435–439 (1950)

    Google Scholar 

  • [Kr] Krein, S.G.: Linear differential equations in Banach space. Transl. Math. Mon.27 (1972)

  • [L] Laughlin, R.B.: Quantized Hall conductivity in two dimensions. Phys. Rev. B23, 5632–5633 (1981)

    Google Scholar 

  • [TKN2] Thouless, D.J., Kohmoto, M., Nightingale, M., den-Nys, M.: Quantized Hall conductance in a two dimensional periodic potential. Phys. Rev. Lett.49, 405–408 (1982)

    Google Scholar 

  • [TN1] Thouless, D.J., Niu, Q.: Nonlinear corrections to the quantization of Hall conductance. Phys. Rev. B30, 3561–3562 (1984)

    Google Scholar 

  • [TN2] Thouless, D.J., Niu, Q.: Quantised adiabatic charge transport in the presence of substrate disorder and many-body interaction. J. Phys. A17, 2453–2462 (1984)

    Google Scholar 

  • [Y] Yoshida, K.: Functional analysis. Grundlehren der math. Wiss. Bd. 123, Berlin, Heidelberg, New York: Springer

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Authors and Affiliations

  1. Fachbereich Mathematik MA 7-2, Technische Universität Berlin, D-1000, Berlin 12

    M. Klein & R. Seiler

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  1. M. Klein
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  2. R. Seiler
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Communicated by B. Simon

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Klein, M., Seiler, R. Power-law corrections to the Kubo formula vanish in quantum Hall systems. Commun.Math. Phys. 128, 141–160 (1990). https://doi.org/10.1007/BF02097050

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  • DOI: https://doi.org/10.1007/BF02097050

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