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arXiv · 0810.2277

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

Charlotte Gils·Eddy Ardonne·Simon Trebst·Andreas W. W. Ludwig·Matthias Troyer·Zhenghan Wang
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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.

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Charlotte Gils, Eddy Ardonne, Simon Trebst, Andreas W. W. Ludwig, Matthias Troyer, Zhenghan Wang. 2009-06-19. Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids. https://doi.org/10.1103/physrevlett.103.070401

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