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

TL;DR

This paper explores the properties of su(2)_k anyon systems, revealing their topological protection, phase diagrams, and the nucleation of 2D topological liquids, with implications for quantum Hall states and edge modes.

Contribution

It establishes a connection between anyonic chains and spin systems, detailing their phase diagrams and topological features, and describes the nucleation of topological liquids within quantum Hall states.

Findings

Anyonic spin-1/2 chains have topological protection stabilizing gapless states.

Anyonic spin-1 chains exhibit phase diagrams similar to biquadratic spin-1 chains.

Nucleation of 2D topological liquids occurs within non-Abelian quantum Hall states.

Abstract

Quantum mechanical systems, whose degrees of freedom are so-called su(2)_k anyons, form a bridge between ordinary SU(2) spin systems and systems of interacting non-Abelian anyons. Such a connection can be made for arbitrary spin-S systems, and we explicitly discuss spin-1/2 and spin-1 systems. 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 infinity) of the ordinary spin-1/2 Heisenberg chain. For anyonic spin-1 chains we find their phase diagrams to closely mirror 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 of 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.