Hall effect, edge states and Haldane exclusion statistics in two-dimensional space
F. Ye, P. A. Marchetti, Z. B. Su, L. Yu
TL;DR
This paper explores the connection between braid and Haldane exclusion statistics in two-dimensional systems, demonstrating the existence of HES in incompressible anyon liquids with Hall response and highlighting the role of edge states.
Contribution
It provides a non-perturbative proof of HES in incompressible anyon liquids and analyzes the impact of edge states on HES in a quantum anomalous Hall model.
Findings
HES exists for incompressible anyon liquids with Hall response
Edge states are crucial for HES in quantum anomalous Hall systems
Perturbative analysis reveals the role of edge states in statistical properties
Abstract
We clarify the relation between two kinds of statistics for particle excitations in planar systems: the braid statistics of anyons and the Haldane exclusion statistics(HES). It is shown non-perturbatively that the HES exists for incompressible anyon liquid in the presence of a Hall response. We also study the statistical properties of a specific quantum anomalous Hall model with Chern-Simons term by perturbation in both compressible and incompressible regimes, where the crucial role of edge states to the HES is shown.
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