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.

arXiv comment7 pages, 5 figures

References in corpus (53)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological orders and Edge excitations in FQH states
• Zoo of quantum-topological phases of matter
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Topological Origin of Equatorial Waves
• Impurity scattering and transport of fractional Quantum Hall edge state
• Topological charge pumping in a one-dimensional optical lattice
• Manipulation of Dirac Cones in Mechanical Graphene
• Quantized Berry Phases as Local Order Parameters of Quantum Liquids
• Reconstruction of Fractional Quantum Hall Edges
• Edge reconstruction in the fractional quantum Hall regime
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Topological fractional pumping with alkaline-earth(-like) ultracold atoms
• Charge Pumping of Interacting Fermion Atoms in the Synthetic Dimension
• A Characterization of Topological Insulators: Chern Numbers for a Ground State Multiplet
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Explicit Gauge Fixing for Degenerate Multiplets: A Generic Setup for Topological Orders
• Sum Rule of the Hall Conductance in Random Quantum Phase Transition
• Anomalous Topological Active Matter
• Fractional topological states of dipolar fermions in one-dimensional optical superlattices
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Bulk-edge correspondence in topological pumping
• Square-root topological semimetals
• Fractional topological phase in one-dimensional flatbands with nontrivial topology
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Edge-mode velocities and thermal coherence of quantum Hall interferometers
• Edge reconstructions in fractional quantum Hall systems
• Quantized Berry Phases for a Local Characterization of Spin Liquids in Frustrated Spin Systems
• $Z_N$ Berry Phases in Symmetry Protected Topological Phases
• Interaction Induced Topological Charge Pump
• Fractional Edge Reconstruction in Integer Quantum Hall Phases
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Abelian topological order of $\nu =2/5$ and $3/7$ fractional quantum Hall states in lattice models
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Effective Edge State Dynamics in the Fractional Quantum Hall Effect
• Bosonic integer quantum Hall effect as topological pumping
• Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
• Density matrix renormalization group study of the $\nu =1/3$ edge states in fractional quantum Hall systems
• Fractional Topological States in Quantum Spin Chains with Periodical Modulation
• Plateau transitions of spin pump and bulk-edge correspondence
• Adiabatic Construction of Hierarchical Quantum Hall States
• Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula
• 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