Block entanglement in 1D quantum chains — critical vs gapped phases
For a gapped 1D system, the entanglement entropy S(l) of a block of l sites saturates to a constant: S ~ const (area law). At a critical point (CFT), S ~ (c/3) log(l) + const, where c is the central charge (c=1 for XX model). For a volume-law state (e.g., random pure state), S ~ l/2. The coefficient c is a universal fingerprint of the universality class of the quantum critical point.