Thermodynamic behavior of braiding statistics for certain fractional quantum Hall quasiparticles

It is widely believed that the braiding statistics of the quasiparticles of the fractional quantum Hall effect is a robust, topological property, independent of the details of the Hamiltonian or the wave function. However, for the quasiparticles of the 1/3 state, an explicit evaluation of the braiding phases using Laughlin's wave function has not produced a well-defined braiding statistics. We revisit this issue and demonstrate that the expected braiding statistics is recovered in the thermodynamic limit for exchange paths that are of finite extent but not for macroscopically large exchange loops that encircle a finite fraction of electrons. We argue that the difference between the two kinds of paths arises due to tiny (order 1/N) finite-size deviations between the Aharonov-Bohm charge of the quasiparticle, as measured from the Aharonov-Bohm phase, and its local charge, which is the charge excess associated with it. An implication of our work is that models for quasiparticles that produce identical local charge can lead to different braiding statistics, which therefore can, in principle, be used to distinguish between such models.