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

TL;DR

This paper explores the phase diagrams and topological properties of su(2)_k anyonic spin-1 chains, revealing parallels with ordinary spin-1 chains and identifying unique topological protections and effects related to the deformation parameter k.

Contribution

It introduces a detailed analysis of anyonic generalizations of spin-1 chains, highlighting new topological symmetries and effects not present in traditional models.

Findings

Phase diagrams mirror those of ordinary spin-1 chains

Identification of a topological symmetry protecting gapless phases

Discovery of even/odd effects related to the parameter k

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.