Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain

Understand

Topological insulators supporting non-abelian anyonic excitations are at the center of attention as candidates for topological quantum computation.

• In this paper, we analyze the ground-state properties of disordered non-abelian anyonic chains.
• The resemblance of fusion rules of non-abelian anyons and real space decimation strongly suggests that disordered chains of such anyons generically exhibit infinite-randomness phases.
• Concentrating on the disordered golden chain model with nearest-neighbor coupling, we show that Fibonacci anyons with the fusion rule $\tau\otimes\tau={\bf 1}\oplus \tau$ exhibit two infinite-randomness phases: a random-singlet phase when all bonds prefer the trivial fusion channel, and a mixed phase which occurs whenever a finite density of bonds prefers the $\tau$ fusion channel.