Entanglement Entropy & Area Law — 1D

For a 1D chain of N qubits in random states, the von Neumann entanglement entropy S(A) = −Tr(ρ_A log ρ_A) of a contiguous block A. The area law says S ∝ constant (gapped); critical systems violate it: S ~ (c/3)log(ℓ). Explore how block size and correlations shape the entropy profile.

Chain N 40 Correlation ξ 0.0 Central charge c 1.0 Mode

Area law: S(ℓ) ≈ const | CFT / critical: S(ℓ) ≈ (c/3) ln[N/π · sin(πℓ/N)] | Volume law: S(ℓ) ≈ s₀ · min(ℓ, N−ℓ)