Domain-wall-type defects as anyons in phase space

We discuss how the braiding properties of Laughlin quasiparticles in quantum Hall states can be understood within a one-dimensional formalism we proposed earlier. In this formalism, the two-dimensional space of the Hall liquid is identified with the phase space of a one-dimensional lattice system, and localized Laughlin quasiholes can be understood as coherent states of lattice solitons. The formalism makes comparatively little use of the detailed structure of Laughlin wave functions, and may offer ways to be generalized to non-Abelian states.