Elaborating the phase diagram of spin-1 anyonic chains

TL;DR

This paper revisits the phase diagram of spin-1 $su(2)_k$ anyonic chains, revealing new phase transitions, critical points, and phases using integrability and Bethe ansatz techniques.

Contribution

It uncovers previously overlooked integrable points, identifies new first order transitions, and describes a novel $Z_k$ parafermionic critical point in spin-1 anyonic chains.

Findings

Discovery of new first order phase transitions

Identification of a $Z_k$ parafermionic critical point

Revelation of additional phases beyond previous conjectures

Abstract

We revisit the phase diagram of spin-1 $su(2)_k$ anyonic chains, originally studied by Gils {\it et. al.} [Phys. Rev. B, {\bf 87} (23) (2013)]. These chains possess several integrable points, which were overlooked (or only briefly considered) so far. Exploiting integrability through a combination of algebraic techniques and exact Bethe ansatz results, we establish in particular the presence of new first order phase transitions, a new critical point described by a $Z_k$ parafermionic CFT, and of even more phases than originally conjectured. Our results leave room for yet more progress in the understanding of spin-1 anyonic chains.