Anyons on a Lattice
Anyons on the square lattice are studied numerically. We treat several different boundary conditions. These boundary conditions define different topological structures such as planc(plate), annulus (cylinder) and torus. To realize the system consistently, we start from a braid group analysis. The system is characterized not only by the anyon statistics θ but also by the magnetic fluxes Φx (and Φy) threading through the holes of the system. We generalize the construction to get a system where several species of anyons with θ=0, ±2π/q, ±4π/q,..., (π), exist simultaneously. Explicit numerical calculations are demonstrated.
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