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Fibonacci topological order from quantum nets.

Paul Fendley1, Sergei V Isakov, Matthias Troyer

  • 1Department of Physics, University of Virginia, Charlottesville, Virginia 22904-4714, USA.

Physical Review Letters
|July 16, 2013
PubMed
Summary
This summary is machine-generated.

We analyzed a quantum net model, revealing a non-Abelian topological order. Its excitations are dynamic, unlike fixed ones in similar models, offering a new path for topological quantum computing.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Information Theory
  • Topological Quantum Field Theory

Background:

  • Topological order in quantum systems offers robustness against local perturbations.
  • Non-Abelian topological orders are crucial for topological quantum computing.
  • String-net models provide a framework for realizing topological orders.

Purpose of the Study:

  • To analyze a quantum net model for non-Abelian topological order.
  • To investigate the properties of its ground state and excitations.
  • To develop a Hamiltonian suitable for various lattices with simpler interactions.

Main Methods:

  • Analysis of a quantum net model.
  • Exact diagonalization to provide evidence for a spectral gap.
  • Construction of a Hamiltonian with face, vertex, and Jones-Wenzl terms.

Main Results:

  • The quantum net model exhibits a non-Abelian topological order of doubled-Fibonacci type.
  • The ground state shares topological behavior with string-net models.
  • The developed Hamiltonian is applicable to any lattice and features dynamical excitations.

Conclusions:

  • The study presents a viable model for non-Abelian topological order with practical advantages.
  • The Hamiltonian's design and dynamical excitations are key advancements.
  • This work contributes essential components for realizing topological order.