Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model

Recent studies have shown that logarithmic divergence of entanglement entropy as a function of the size of a subsystem is a signature of criticality in quantum models. We demonstrate that the ground-state entanglement entropy of n sites for the ferromagnetic Heisenberg spin-1/2 chain of the length L in a sector with fixed magnetization y per site grows as 1/2log₂[n(L-n)∕L]C(y), where C(y)=2πe(1/4-y²).