Area law scaling for the entropy of disordered quasifree fermions.

We study theoretically and numerically the entanglement entropy of the d-dimensional free fermions whose one-body Hamiltonian is the Anderson model. Using the basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy ⟨S(Λ)⟩ of the d dimension cube Λ of side length l admits the area law scaling ⟨S(Λ)⟩ ∼ l((d-1)),l ≫ 1, even in the gapless case, thereby manifesting the area law in the mean for our model. For d = 1 and l ≫ 1 we obtain then asymptotic bounds for the entanglement entropy of typical realizations of disorder and use them to show that the entanglement entropy is not self-averaging, i.e., has nonvanishing random fluctuations even if l ≫ 1.