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arXiv · 1303.4290

Anyonic quantum spin chains: Spin-1 generalizations and topological stability

Charlotte Gils·Eddy Ardonne·Simon Trebst·David A. Huse·Andreas W. W. Ludwig·Matthias Troyer·Zhenghan Wang
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Abstract

There are many interesting parallels between systems of interacting non-Abelian anyons and quantum magnetism, occuring in ordinary SU(2) quantum magnets. Here we consider theories of so-called su(2)_k anyons, well-known deformations of SU(2), in which only the first k+1 angular momenta of SU(2) occur. In this manuscript, we discuss in particular anyonic generalizations of ordinary SU(2) spin chains with an emphasis on anyonic spin S=1 chains. We find that the overall phase diagrams for these anyonic spin-1 chains closely mirror the phase diagram of the ordinary bilinear-biquadratic spin-1 chain including anyonic generalizations of the Haldane phase, the AKLT construction, and supersymmetric quantum critical points. A novel feature of the anyonic spin-1 chains is an additional topological symmetry that protects the gapless phases. Distinctions further arise in the form of an even/odd effect in the deformation parameter k when considering su(2)_k anyonic theories with k>4, as well as for the special case of the su(2)_4 theory for which the spin-1 representation plays a special role. We also address anyonic generalizations of spin-1/2 chains with a focus on the topological protection provided for their gapless ground states. Finally, we put our results into context of earlier generalizations of SU(2) quantum spin chains, in particular so-called (fused) Temperley-Lieb chains.

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Charlotte Gils, Eddy Ardonne, Simon Trebst, David A. Huse, Andreas W. W. Ludwig, Matthias Troyer, Zhenghan Wang. 2013-03-18. Anyonic quantum spin chains: Spin-1 generalizations and topological stability. https://doi.org/10.1103/physrevb.87.235120

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