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

Understand

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.