From the fusion rule τ ⊗ τ = 1 ⊕ τ, the quantum dimension d_τ satisfies d_τ² = 1 + d_τ → d_τ = φ = (1+√5)/2 (golden ratio). Equivalent to φ² − φ − 1 = 0. Hilbert-space dimension of n τ-anyons (all fusing to the trivial sector) is the…
From the fusion rule τ ⊗ τ = 1 ⊕ τ, the quantum dimension d_τ satisfies d_τ² = 1 + d_τ → d_τ = φ = (1+√5)/2 (golden ratio). Equivalent to φ² − φ − 1 = 0. Hilbert-space dimension of n τ-anyons (all fusing to the trivial sector) is the…