Anyonic braiding via quench dynamics in fractional quantum Hall liquids

TL;DR

This paper investigates the dynamics of quasiholes in fractional quantum Hall states after a quench, demonstrating how their braiding statistics can be extracted from time evolution and Berry-phase calculations.

Contribution

It introduces a method to study anyonic braiding via quench dynamics in fractional quantum Hall liquids, including effects of realistic confinement and interactions.

Findings

Quasihole states can be efficiently studied in a reduced Hilbert space.

Quasihole braiding phases can be accurately obtained from Berry-phase calculations.

Quench dynamics reveal the rotation and braiding behavior of anyons.

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.