Abstract
We revisit the phase diagram of spin-1 su(2)_ksu(2)k anyonic chains, originally studied by Gils et. al. . 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_kZk 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.
Highlights
Non-abelian anyons may form collective states with exponentially precise degeneracies that could be used for topological quantum computation [5]
For even sizes L, we find by exact study of small systems that the ground state of the anyonic chain is the same as the ground state of the Potts model, and sits in the 0,1 module
In order to recover the spectrum of the RSOS model from that of the vertex transfer matrix (Hamiltonian), one must consider twisted boundary conditions, parametrized by some twist angle φ, just like we did in the Temperley-Lieb case earlier 7
Summary
Non-Abelian anyons are quasiparticles with exotic braiding statistics which have been proposed to occur as emergent low-energy excitations in certain 2+1-dimensional quantum materials. Non-abelian anyons may form collective states with exponentially precise degeneracies that could be used for topological quantum computation [5] In this context it is of crucial importance to understand how such particles interact, and over the years a lot of attention has been given to one-dimensional anyonic chains with shortrange interactions. We use this opportunity to discuss in detail the obstacles in relating physical properties of models which are based on the same algebra, but with different representations (such as vertex, loop, and anyonic or restricted solid on solid (RSOS) models).
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