Emergent Exclusion Statistics of Fibonacci Anyons in 2D Topological Phases

TL;DR

This paper explores how the generalized Pauli exclusion principle manifests for Fibonacci anyons in 2D topological phases, revealing topology-dependent exclusion statistics and insights into the quasiparticle Hilbert space structure.

Contribution

It constructs and analyzes the fluxon number operator in the Levin-Wen model with Fibonacci data, identifying topology-dependent exclusion statistics parameters.

Findings

Exclusion statistics depend on system topology (sphere or torus).

Constructed the fluxon number operator in the Levin-Wen model.

Revealed the structure of the many-body Hilbert space for Fibonacci anyons.

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.