Entanglement Entropy — Cardy-Calabrese

Area law violation and CFT logarithmic scaling in 1D quantum systems

System size L: Central charge c: UV cutoff ε:

Calabrese & Cardy (2004) showed that the entanglement entropy of a 1D subsystem of length ℓ in a critical CFT ground state scales as S(ℓ) = (c/3)·ln(L/π·sin(πℓ/L)) + const, where c is the central charge. This logarithmic growth (vs. area law S ~ const for gapped systems) is a hallmark of quantum criticality and underlies the difficulty of simulating critical systems with tensor networks.