Multi-anyon quantum mechanics and fractional statistics

Song He

Andrij A. Rovenchak

Taeseung Choi, Jungjai Lee, Chang‐Mo Ryu

We consider the external magnetic field effects on the two types of anyons with fractional statistical parameter p/q with coprimes p and q, one with a fractional charge e/q and the other with a fractional flux p ϕ0/q by exact ground state wave function. We also study the geometry in which a two-dimensional strip of anyons contains an island of anyons with different statistical parameters in their equilibrium. The equilibrium inside an island is shown to be periodic with respect to the magnetic flux through the island. The period for the fractional charge anyon equals to the integer multiple of the fundamental flux quantum. On the other hand, in the case of the fractional flux anyon, the period is found to be the fractional multiple of the fundamental flux quantum.

Diptiman Sen

Torbjörn Einarsson

General kinematical restrictions on quantum-theories of N identical anyons have been established by using braid groups. For an orientable compact surface (without boundary) of genus g, the statistical parameter θ is a rational multiple of π, θ=πp/v (p and v mutually prime integers), and the number of components of the wavefunction is (a multiple of) vg. The particle-number is N=rv+1−g (r integer) for spinless (S=0) and N=rv for spinning (S=θ/2π) anyons. The restrictions for spinning anyons are consistent with results for fractional quantum Hall systems, nonlinear O(3) field theory, and Chern-Simons theory. The multi-component structure, which appears for g≥1, reflects an internal collective degree of freedom. A comparison with the multi-component wavefunctions needed to describe systems with fractionally charged quasi-particles yields consistency relations between charge and statistics. Non-orientable surfaces do not allow fractional statistics.