For a bipartite system A|B, the von Neumann entanglement entropy is
S = −Tr(ρ_A log ρ_A) = −Σ λᵢ log λᵢ
where λᵢ are the eigenvalues of the reduced density matrix ρ_A = Tr_B|ψ⟩⟨ψ|.
Via the Schmidt decomposition, these eigenvalues are squares of the singular values
of the coefficient matrix reshaped from the state vector.
Area law: gapped ground states have S ~ ∂A (constant for 1D chains).
Critical systems (CFT) have S ~ (c/3) log L where c is the central charge.
Maximally entangled state: S = log(min(d_A, d_B)).