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

C. Gils, E. Ardonne, S. Trebst, D. A. Huse, A. W.W. Ludwig, M. Troyer, Z. Wang

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There are many interesting parallels between systems of interacting non-Abelian anyons and quantum magnetism occurring 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 paper, 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≥5, 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-12 chains with a focus on the topological protection provided for their gapless ground states. Finally, we put our results into the context of earlier generalizations of SU(2) quantum spin chains, in particular so-called (fused) Temperley-Lieb chains.

Original languageEnglish (US)
Article number235120
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number23
StatePublished - Jun 17 2013

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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