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

Nature Reviews Physics volume 2, page 723 (2020)Cite this article

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The recently published article (Michalakis, S. Why is the Hall conductance quantized? Nat. Rev. Phys. 2, 392–393 (2020)1) does not accurately convey the full history of the proof of the quantization theorem2. Here I will primarily present my personal history before the work on this paper started, and then briefly discuss my work with Spyridon Michalakis, before mentioning some interesting work that resulted.

The proof results from combining two ideas. First, the elegant proof of Joseph Avron and Ruedi Seiler that the Hall conductance averaged over a ‘flux torus’ of different Aharonov-Bohm fluxes is quantized3. The second idea is to replace the curvature of a connection due to adiabatic evolution considered in3,4 with the curvature of a quasi-adiabatic evolution operator.

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References

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

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

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  1. Microsoft Quantum, Redmond, WA, United States

    Matthew B. Hastings

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  1. Matthew B. Hastings
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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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