Visualize entanglement entropy scaling in 1D quantum systems. Compare area law (gapped), logarithmic (critical/CFT), and volume law (random) states. The area law enables efficient MPS/DMRG simulation.
Entanglement entropy S(l) for interval of length l in a chain of N. Area law (gapped): S=const (Hastings 2007 — provably satisfiable with χ-bounded MPS). Critical (CFT): S=(c/3)log(l) — central charge c counts degrees of freedom (Calabrese-Cardy 2004). Random state: S=l·log(2)-const (volume law). Holographic duality: S=Area(RT surface)/4G (Ryu-Takayanagi formula, 2006).