Anyonic braiding via quench dynamics in fractional quantum Hall liquids

In a Laughlin fractional quantum Hall state, one- and two-quasihole states can be obtained by diagonalizing the many-body Hamiltonian with a trapping potential or, for larger systems, from the linear combination of the edge Jack polynomials. The quasihole states live entirely in the subspace of the...

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Bibliographic Details
Published in:arXiv.org 2022-02
Main Authors: Li, Jie, Ye, Dan, Chen-Xin, Jiang, Jiang, Na, Wan, Xin, Zi-Xiang Hu
Format: Article
Language:English
Subjects:
Braiding
Confinement
Energy spectra
Hilbert space
Polynomials
Trapping
Online Access:Get full text
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Summary:In a Laughlin fractional quantum Hall state, one- and two-quasihole states can be obtained by diagonalizing the many-body Hamiltonian with a trapping potential or, for larger systems, from the linear combination of the edge Jack polynomials. The quasihole states live entirely in the subspace of the lowest-energy branch in the energy spectrum with a fixed number of orbits, or a hard-wall confinement. The reduction in the Hilbert space dimension facilitates the study of time evolution of the quasihole states after, say, the removal of the trapping potential. We explore the quench dynamics under a harmonic external potential, which rotates the quasiholes in the droplet, and discuss the effect of long-range interaction and more realistic confinement. Accurate evaluation of the mutual statistics phase of anyons for a wide range of anyon separation can be achieved from the Berry-phase calculation.
ISSN:2331-8422
DOI:10.48550/arxiv.2202.10006