Collective states of interacting anyons, edge states, and the nucleation of topological liquids

• Published in: Physical review letters Vol. 103; no. 7; p. 070401
• Main Authors: Gils, Charlotte, Ardonne, Eddy, Trebst, Simon, Ludwig, Andreas W W, Troyer, Matthias, Wang, Zhenghan
• Format: Journal Article
• Language: English
• Published: United States 14.08.2009
• ISSN: 0031-9007
• DOI: 10.1103/physrevlett.103.070401

Quantum mechanical systems, whose degrees of freedom are so-called 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-->infinity) 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.