Fibonacci topological order from quantum nets

Abstract

We analyze a model of quantum nets and show it has non-abelian topological order of doubled Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined on any lattice, has less complicated interactions, and its excitations are dynamical, not fixed. This Hamiltonian includes terms acting on the spins around a face, around a vertex, and special "Jones-Wenzl" terms that serve to couple long loops together. We provide strong evidence for a gap by exact diagonalization, completing the list of ingredients necessary for topological order.

5 pages. v2: minor rewriting

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Cited by in corpus (10)

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Introduction to topological quantum computation with non-Abelian anyons
• Condensation-Driven Phase Transitions in Perturbed String Nets
• Tensor network approach to phase transitions of a non-Abelian topological phase
• Simulating topological tensor networks with Majorana qubits
• Stability and Loop Models from Decohering Non-Abelian Topological Order
• Russian doll spectrum in a non-Abelian string-net ladder
• Quantum criticality of loops with topologically constrained dynamics
• Projected Entangled Pair States with continuous virtual symmetries
• Unveiling topological order through multipartite entanglement