Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids

Quantum mechanical systems, whose degrees of freedom are so-called $\mathrm{su}(2{)}_k$ anyons, form a bridge between ordinary SU(2) quantum magnets (of arbitrary spin-$S$) and systems of interacting non-Abelian anyons. Anyonic spin-$1/2$ chains exhibit a topological protection mechanism that stabilizes their gapless ground states and which vanishes only in the limit ($k\to \infty$) of the ordinary spin-$1/2$ Heisenberg chain. For anyonic spin-1 chains the phase diagram closely mirrors the one of the biquadratic SU(2) spin-1 chain. Our results describe, at the same time, nucleation of different 2D topological quantum fluids within a “parent” non-Abelian quantum Hall state, arising from a macroscopic occupation with localized, interacting anyons. The edge states between the “nucleated” and the parent liquids are neutral, and correspond precisely to the gapless modes of the anyonic chains.