Abstract
Quantum gates for the manipulation of topological qubits rely on interactions between non-Abelian anyonic quasiparticles. We study the collective behavior of systems of anyons arising from such interactions. In particular, we study the effect of favoring different fusion channels of the screened Majorana spins appearing in the recently proposed topological Kondo effect. Based on the numerical solution of a chain of $SO{(5)}_{2}$ anyons we identify two critical phases whose low-energy behavior is characterized by conformal field theories with central charges $c=1$ and $c=8/7$, respectively. Our results are complemented by exact results for special values of the coupling constants which provide additional information about the corresponding phase transitions.
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