Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions

Abstract

We consider the effect of quenched spatial disorder on systems of interacting, pinned non-Abelian anyons as might arise in disordered Hall samples at filling fractions ν=5/2 or ν=12/5. In one spatial dimension, such disordered anyon models have previously been shown to exhibit a hierarchy of infinite randomness phases. Here, we address systems in two spatial dimensions and report on the behavior of Ising and Fibonacci anyons under the numerical strong-disorder renormalization group (SDRG). In order to manage the topology-dependent interactions generated during the flow, we introduce a planar approximation to the SDRG treatment. We characterize this planar approximation by studying the flow of disordered hard-core bosons and the transverse field Ising model, where it successfully reproduces the known infinite randomness critical point with exponent ψ~ 0.43. Our main conclusion for disordered anyon models in two spatial dimensions is that systems of Ising anyons as well as systems of Fibonacci anyons do not realize infinite randomness phases, but flow back to weaker disorder under the numerical SDRG treatment.

arXiv comment12 pages, 12 figures, 1 table

References in corpus (30)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Majorana fermions in a tunable semiconductor device
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
• Interacting anyons in topological quantum liquids: The golden chain
• Infinite-randomness quantum Ising critical fixed points
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• A short introduction to Fibonacci anyon models
• Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Particle-hole symmetric localization in two dimensions
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Infinite disorder scaling of random quantum magnets in three and higher dimensions
• Infinite-Randomness Fixed Points for Chains of Non-Abelian Quasiparticles
• Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level
• Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state
• Disorder-induced Majorana metal in interacting non-Abelian anyon systems
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Majorana fermions of a two-dimensional Px+iPy superconductor
• Splitting the Topological Degeneracy of non-Abelian Anyons
• Infinite Randomness Phases and Entanglement Entropy of the Disordered Golden Chain
• Permutation Symmetric Critical Phases in Disordered Non-Abelian Anyonic Chains

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