2008/07/08 by Lukasz Fidkowski, Gil Refael, N. E. Bonesteel +3
Mathematics · Physics and Astronomy · #Abelian group #Central charge #Combinatorics #Fibonacci number #Fixed point #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Randomness #Renormalization group #Singlet state #Statistics #Theoretical and Computational Physics #Topological quantum computer #cond-mat.dis-nn #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.78.224204
16 pages
arxiv created 2008/07/08 · openalex publication_date 2008/12/18 · arxiv updated 2013/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Topological insulators supporting non-Abelian anyonic excitations are in 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 \ensuremathτ\ensuremath\bigotimes\ensuremathτ=1\ensuremath\bigoplus\ensuremathτ 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 \ensuremathτ fusion channel. Real-space renormalization-group (RG) analysis shows that the random-singlet fixed point is unstable to the mixed fixed point. By analyzing the entanglement entropy of the mixed phase, we find its effective central charge and find that it increases along the RG flow from the random-singlet point, thus ruling out a c theorem for the effective central charge.