Anyonic braiding via quench dynamics in fractional quantum Hall liquids

Abstract

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.

9 pages, 9 figures

References in corpus (11)

• Non-Abelian Anyons and Topological Quantum Computation
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Cited by in corpus (5)

• Spin-statistics relation and the Abelian braiding phase for anyons in fractional quantum Hall effect
• Braiding fractional quantum Hall quasiholes on a superconducting quantum processor
• Dynamics of quasiholes and quasiparticles at the edges of small lattices
• Complexity of the Laughlin wave function from the Dyson-orbital perspective
• Developments in the applications of density functional theory to fractional quantum Hall systems