Ising anyons with a string tension

Abstract

We consider the string-net model on the honeycomb lattice for Ising anyons in the presence of a string tension. This competing term induces a nontrivial dynamics of the non-Abelian anyonic quasiparticles and may lead to a breakdown of the topological phase. Using high-order series expansions and exact diagonalizations, we determine the robustness of this doubled Ising phase which is found to be separated from two gapped phases. An effective quantum dimer model emerges in the large tension limit giving rise to two different translation symmetry-broken phases. Consequently, we obtain four transition points, two of which are associated with first-order transitions whereas the two others are found to be continuous and provide examples of recently proposed Bose condensation for anyons.

10 pages, 8 figures, typos corrected

References in corpus (4)

• Condensate induced transitions between topologically ordered phases
• A theory of topological edges and domain walls
• Topological Phase Transitions in the Golden String-Net Model
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids

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• Phase diagram of an extended quantum dimer model on the hexagonal lattice
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• Probing many-body localization in a disordered quantum dimer model on the honeycomb lattice
• Mean-field ansatz for topological phases with string tension
• Monte Carlo based techniques for quantum magnets with long-range interactions
• Boson condensation and instability in the tensor network representation of string-net states
• Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps
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• Linked Cluster Expansions via Hypergraph Decompositions
• Wegner-Wilson loops in string nets
• Bound states in string nets
• Topological and nontopological degeneracies in generalized string-net models
• Ising versus $SU(2{)}_2$ string-net ladder
• Quantum phase transitions to topological Haldane phases in spin-one chains studied by linked-cluster expansions