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A different perspective on the history of the proof of Hall conductance quantization

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References

  1. Michalakis, S. Why is the Hall conductance quantized? Nat. Rev. Phys. 2, 392–393 (2020).

    Article  Google Scholar 

  2. Hastings, M. B. & Michalakis, S. Quantization of hall conductance for interacting electrons on a torus. Commun. Math. Phys. 334, 433–471 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  3. Avron, J. E. & Seiler, R. Quantization of the Hall conductance for general, multiparticle Schrodinger hamiltonians. Phys. Rev. Lett. 54, 259 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  4. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405 (1982).

    Article  ADS  Google Scholar 

  5. Hastings, M. B. Lieb-Schultz-Mattis in higher dimensions. Phys. Rev. B 69, 104431 (2004).

    Article  ADS  Google Scholar 

  6. Misguich, G. and Lhuillier, C. Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions. Preprint at: https://arxiv.org/abs/cond-mat/0002170 (2000).

  7. Oshikawa, M. Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice. Phys. Rev. Lett. 84, 1535 (2000).

    Article  ADS  Google Scholar 

  8. Osborne, T. J. Simulating adiabatic evolution of gapped spin systems. Phys. Rev. A 75, 032321 (2007).

    Article  ADS  Google Scholar 

  9. Ingham, A. E. A note on Fourier transforms. J. Lond. Math. Soc. 1, 29–32 (1934).

    Article  MathSciNet  Google Scholar 

  10. Bravyi, S. & Hastings, M. B. A short proof of stability of topological order under local perturbations. Commun. Math. Phys. 307, 609 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  11. Michalakis, S. & Zwolak, J. P. Stability of frustration-free Hamiltonians. Commun. Math. Phys. 322, 277–302 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  12. Michalakis, S. Stability of the area law for the entropy of entanglement. Preprint at: https://arxiv.org/abs/1206.6900 (2012).

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Correspondence to Matthew B. Hastings.

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Hastings, M.B. A different perspective on the history of the proof of Hall conductance quantization. Nat Rev Phys 2, 723 (2020). https://doi.org/10.1038/s42254-020-00255-5

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