Adiabatic insertion of the Aharonov-Bohm flux through two pinholes introduces charge transport between them when the system is topologically non-trivial. This is the Laughlin argument. The defects/pinholes are the boundaries of the system and the behavior of the edge states tells us how much the charge is carried that further corresponds to the many-body Chern numbers as the bulk-edge correspondence. This is explicitly confirmed for the quantum Hall effects of anyons connecting well-known integer/fractional quantum Hall states by transmuting the statistical fluxes of particles into an external magnetic field (adiabatic heuristic argument). The paper Bulk-edge correspondence in the adiabatic heuristic principle” by Koji Kudo, Yoshihito Kuno, and Yasuhiro Hatsugai has been accepted for publication in Physical Review B as Letters on 14 December 2021 and has been published on Published 28 December 2021. See also arXiv:2106.10459.
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