Emergent Exclusion Statistics of Fibonacci Anyons in 2D Topological Phases

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.

8 pages, 2 figure; v2. References and note added; v3. Supplementary material added

References in corpus (3)

• Topological Phase Transitions in the Golden String-Net Model
• Topology driven quantum phase transitions in time-reversal invariant anyonic quantum liquids
• Exactly Solvable Lattice Models with Crossing Symmetry

Cited by in corpus (8)

• Full Dyon Excitation Spectrum in Generalized Levin-Wen Models
• Partition function of the Levin-Wen model
• Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases
• Topological and nontopological degeneracies in generalized string-net models
• Anyon exclusions statistics on surfaces with gapped boundaries
• Finite-temperature properties of string-net models
• Fractional Exclusion Statistics as an Occupancy Process
• Nonlinear Symmetry-Fragmentation of Nonabelian Anyons In Symmetry-Enriched Topological Phases: A String-Net Model Realization