Area law vs. volume law entanglement across quantum phases
Entanglement entropy S(A) = -Tr[ρ_A ln ρ_A] obeys an area law S ~ L^(d-1) for gapped phases and a logarithmic law S ~ (c/3)ln(L) for 1D critical systems (CFT), where c is central charge. Random states obey a volume law S ~ L^d — maximally entangled. This scaling probes quantum phase transitions.