On anyon phases (specifically in the quantum Hall effect) as Berry phases of a adiabatic transport of anyon positions:
“The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem.”
The model of anyon statistics as an Aharonov-Bohm effect of a “fictitious gauge field” sourced by and coupled to each anyon:
On the quantum Hall effect:
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