Bulk-edge Correspondence in the Adiabatic Heuristic Principle

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.

7 pages, 5 figures

References in corpus (8)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Density matrix renormalization group study of the $\nu =1/3$ edge states in fractional quantum Hall systems
• Adiabatic Construction of Hierarchical Quantum Hall States
• Plateau transitions of spin pump and bulk-edge correspondence
• Entanglement spectrum edge reconstruction and correlation hole of the FQH liquids

Cited by in corpus (4)

• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Adiabatic Continuity of the Spinful Quantum Hall States
• Superconductivity in a system of interacting spinful semions
• Crossover from Integer to Fractional Quantum Hall Effect