Bulk-edge Correspondence in the Adiabatic Heuristic Principle

TL;DR

This paper numerically demonstrates that center-of-mass discontinuities serve as invariants in flux-attachment processes, supporting the bulk-edge correspondence and stability of quantum Hall edge states in the fractional quantum Hall effect.

Contribution

It introduces a numerical approach using Laughlin's argument to verify invariants during flux-attachment, confirming the stability of edge states and the bulk-edge correspondence in fractional quantum Hall systems.

Findings

Center-of-mass discontinuities are invariant during flux-attachment.

Edge state features remain unchanged while topological degeneracy varies.

Supports the stability of quantum Hall edge states in adiabatic processes.

Abstract

Using the Laughlin's argument on a torus with two pin-holes, 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 the 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.