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  • Letter

Bulk-edge correspondence in the adiabatic heuristic principle

Koji Kudo1,2,*, Yoshihito Kuno1,†, and Yasuhiro Hatsugai1,2

  • 1Department of Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan
  • 2Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

  • *Present address: Department of Physics, 104 Davey Lab, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
  • †Present address: Graduate School of Engineering Science, Akita University, Akita 010-8502, Japan.
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Phys. Rev. B 104, L241113 – Published 28 December, 2021

DOI: https://doi.org/10.1103/PhysRevB.104.L241113

Abstract

Using the Laughlin's argument on a torus with two pinholes, we numerically demonstrate that the discontinuities of the center of mass work well as an invariant of the pumping phenomena during the process of the flux attachment, trading the magnetic flux for a statistical one. This is consistent with the bulk-edge correspondence of the fractional quantum Hall effect of anyons. We also confirm that the general feature of the edge states remains unchanged during the process while the topological degeneracy is discretely changed. This supports the stability of the quantum Hall edge states in the adiabatic heuristic principle.

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Phys. Rev. B 104, L241113– Published 28 December, 2021
  • Received 22 June 2021
  • Accepted 14 December 2021
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