A string-net framework constructs exactly solvable SET lattice models from intrinsic categorical symmetries, including a nonabelian S3-enriched example whose gauging produces the S4 quantum-double phase.
Emergent Exclusion Statistics of Fibonacci Anyons in 2D Topological Phases
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abstract
We demonstrate how the generalized Pauli exclusion principle emerges for quasiparticle excitations in 2d topological phases. As an example, we examine the Levin-Wen model with the Fibonacci data (specified in the text), and construct the number operator for fluxons living on plaquettes. By numerically counting the many-body states with fluxon number fixed, the matrix of exclusion statistics parameters is identified and is shown to depend on the spatial topology (sphere or torus) of the system. Our work reveals the structure of the (many-body) Hilbert space and some general features of thermodynamics for quasiparticle excitations in topological matter.
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Symmetry-Enriched Topological Phases and Their Gauging: A String-Net Model Realization
A string-net framework constructs exactly solvable SET lattice models from intrinsic categorical symmetries, including a nonabelian S3-enriched example whose gauging produces the S4 quantum-double phase.