Adrian Feiguin

Publications (3)14.74 Total impact

• Article: One-dimensional itinerant interacting non-Abelian anyons

  Didier Poilblanc, Adrian Feiguin, Matthias Troyer, Eddy Ardonne, Parsa Bonderson
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  ABSTRACT: We construct models of interacting itinerant non-Abelian anyons moving along one-dimensional chains. We focus on itinerant Ising (Majorana) and Fibonacci anyons, which are, respectively, related to SU(2)_2 and SU(2)_3 anyons and also, respectively, describe quasiparticles of the Moore-Read and Z_3-Read-Rezayi fractional quantum Hall states. Following the derivation of the electronic large-U effective Hubbard model, we derive effective anyonic t-J models for the low-energy sectors. Solving these models by exact diagonalization, we find a fractionalization of the anyons into charge and (neutral) anyonic degrees of freedom -- a generalization of spin-charge separation of electrons which occurs in Luttinger liquids. A detailed description of the excitation spectrum can be performed by combining spectra for charge and anyonic sectors. The anyonic sector is the one of a squeezed chain of localized interacting anyons, and hence is described by the same conformal field theory (CFT), with central charge c=1/2 for Ising anyons and c=7/10 or c=4/5 for Fibonacci anyons with antiferromagnetic or ferromagnetic coupling, respectively. The charge sector is the spectrum of a chain of hardcore bosons subject to phase shifts which coincide with the momenta of the combined anyonic eigenstates, revealing a subtle coupling between charge and anyonic excitations at the microscopic level (which we also find to be present in Luttinger liquids), despite the macroscopic fractionalization. The combined central charge extracted from the entanglement entropy between segments of the chain is shown to be 1+c, where c is the central charge of the underlying CFT of the localized anyon (squeezed) chain.
  10/2012;
• Source

  Available from: arxiv.org

  Article: Collective states of interacting Fibonacci anyons.

  Simon Trebst, Eddy Ardonne, Adrian Feiguin, David A Huse, Andreas W W Ludwig, Matthias Troyer
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  ABSTRACT: We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In particular, we generalize the Majumdar-Ghosh Hamiltonian to anyonic degrees of freedom by extending recently studied pairwise anyonic interactions to three-anyon exchanges. The energetic competition between two- and three-anyon interactions leads to a rich phase diagram that harbors multiple critical and gapped phases. For the critical phases and their higher symmetry end points we numerically establish descriptions in terms of two-dimensional conformal field theories. A topological symmetry protects the critical phases and determines the nature of gapped phases.
  Physical Review Letters 09/2008; 101(5):050401. · 7.37 Impact Factor
• Source

  Available from: arxiv.org

  Article: Interacting anyons in topological quantum liquids: the golden chain.

  Adrian Feiguin, Simon Trebst, Andreas W W Ludwig, Matthias Troyer, Alexei Kitaev, Zhenghan Wang, Michael H Freedman
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  ABSTRACT: We discuss generalizations of quantum spin Hamiltonians using anyonic degrees of freedom. The simplest model for interacting anyons energetically favors neighboring anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring neighboring spins to form spin singlets. Numerical simulations of a chain of Fibonacci anyons show that the model is critical with a dynamical critical exponent z=1, and described by a two-dimensional (2D) conformal field theory with central charge c=7/10. An exact mapping of the anyonic chain onto the 2D tricritical Ising model is given using the restricted-solid-on-solid representation of the Temperley-Lieb algebra. The gaplessness of the chain is shown to have topological origin.
  Physical Review Letters 05/2007; 98(16):160409. · 7.37 Impact Factor