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

Laumann, C. R. and Huse, D. A. and Ludwig, A. W. W. and Refael, G. and Trebst, S. and Troyer, M. (2012) Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions. Physical Review B, 85 (22). Art. No. 224201. ISSN 1098-0121.

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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 ≈ 0.49. 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.

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Additional Information:© 2012 American Physical Society. Received 16 March 2012; published 5 June 2012. C.R.L. acknowledges support from a Lawrence Gollub fellowship and the NSF through a grant for the Institute for Theoretical Atomic and Molecular Physics (ITAMP) at Harvard University. D.A.H. was supported, in part, by NSF Grant No. DMR-0819860. A.W.W.L. was supported, in part, by NSF Grant No. DMR-0706140. G.R. was supported, in part, by the Packard Foundation and the IQIM, and an NSF PFC with support of the Moore Foundation.
Group:IQIM, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Lawrence Gollub FellowshipUNSPECIFIED
Harvard UniversityUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Classification Code:PACS number(s): 73.43.−f, 75.10.Nr, 72.15.Rn, 03.65.Vf
Record Number:CaltechAUTHORS:20120515-151935679
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31480
Deposited By: Tony Diaz
Deposited On:27 Jun 2012 18:39
Last Modified:09 Jan 2016 01:17

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