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.
It has been shown that effective lowering of dimension underlies ground-state space structure and properties of two-dimensional lattice systems with a long-range interparticle repulsion. On the basis of this fact a rigorous general procedure has been developed to describe the ground state of the systems.PACS number(s): 64.60. Cn,
We consider the macroscopic system of free lattice fermions in one dimensions assuming that the one-body Hamiltonian of the system is the one dimensional discrete Schrödinger operator with independent identically distributed random potential. We show that the variance of the entanglement entropy of the segment [−M, M ] of the system is bounded away from zero as M → ∞. This manifests the absence of the selfaveraging property of the entanglement entropy in our model, meaning that in the one-dimensional case the complete description of the entanglement entropy is provided by its whole probability distribution. This also may be contrasted the case of dimension two or more, where the variance of the entanglement entropy per unit surface area vanishes as M → ∞ [6], thereby guaranteing the representativity of its mean for large M in the multidimensional case.PACS numbers 03.67. Mn, 03.67, 05.30.Fk, 72.15.Rn
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.