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.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.

Physical Review BJan 12, 201013 citations

Fractional Statistics in Quantum Mechanics

Daniel P. Arovas

Series of the Centro de Estudios Científicos de SantiagoJan 1, 19920 citations

The Aharonov–Bohm effect and fractional statistics of distinguishable particles

Stefan V. Mashkevich

In two-dimensional space, the topological coupling arising between charged particles with attached magnetic fluxes, via the Aharonov–Bohm effect, causes distinguishable particles to effectively acquire quantum statistics: a nontrivial quantum phase is generated when a particle of one species encircles one of a different species. We discuss a number of exact and numerical results concerning distinguishable particles with fractional statistics. Just like for anyons, the spectrum of such particles confined to the lowest Landau level of a strong magnetic field can be found exactly. Then a system of particles in the presence of static magnetic fluxes (equivalent to particles with infinite mass) is considered, and the low-lying states of one particle in the presence of two fluxes and two particles in the presence of one flux are analyzed.In two-dimensional space, the topological coupling arising between charged particles with attached magnetic fluxes, via the Aharonov–Bohm effect, causes distinguishable particles to effectively acquire quantum statistics: a nontrivial quantum phase is generated when a particle of one species encircles one of a different species. We discuss a number of exact and numerical results concerning distinguishable particles with fractional statistics. Just like for anyons, the spectrum of such particles confined to the lowest Landau level of a strong magnetic field can be found exactly. Then a system of particles in the presence of static magnetic fluxes (equivalent to particles with infinite mass) is considered, and the low-lying states of one particle in the presence of two fluxes and two particles in the presence of one flux are analyzed.

Journal of Physics A Mathematical and TheoreticalAug 12, 20100 citations

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.