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Bulletin of the American Physical Society

Disordered Pinned Anyons in Two Dimensions

Chris R. Laumann, David A. Huse, Andreas Ludwig, Gil Refael, Simon Trebst, Matthias Troyer

Published Mar 23, 2011• 0 citations
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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 $\ensuremath{\nu}=5/2$ or $\ensuremath{\nu}=12/5$. 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 $\ensuremath{\psi}\ensuremath{\approx}0.49$. 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.
We consider the interplay of the elastic pinning and the Anderson localization in the transport properties of a charge-density wave in one dimension, within the framework of the Luttinger model in the limit of strong repulsion. We address a conceptually important issue of which of the two disorder-induced phenomena limits the mobility more effectively. We argue that the interplay of the classical and quantum effects in transport of a very rigid charge-density wave is quite nontrivial: the quantum localization sets in at a temperature much smaller than the pinning temperature, whereas the quantum localization length is much smaller than the pinning length.
Abstract The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-N technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii–Kosterlitz–Thouless phase transition in the clean limit at large N. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.