Abstract
We calculate numerically the entanglement entropy of free fermion ground states in one-, two-, and three-dimensional Anderson models and find that it obeys the area law as long as the linear size of the subsystem is sufficiently larger than the mean free path. This result holds in the metallic phase of the three-dimensional Anderson model, where the mean free path is finite although the localization length is infinite. Relation between the present results and earlier ones on area law violation in special one-dimensional models that support metallic phases is discussed.
Highlights
Recent years have witnessed tremendous progress in the study of entanglement in condensed matter/many-body physics
For w > 0, entanglement entropy (EE) grows with L in a manner similar to the disorder free case up to some point and saturates, indicating area law is obeyed for sufficiently large system sizes
We find substantial deviation starts when the system size L reaches the mean free path l, and saturation occurs around L ≈ 3l
Summary
Recent years have witnessed tremendous progress in the study of entanglement in condensed matter/many-body physics Among these studies, free fermion systems play a very special role [1]. In a recent work [7] we studied two very special (onedimensional) 1D models that exhibit free fermion metalinsulator transition (MIT) and found area law violation in the metallic phase, despite the presence of disorder, and absence of sharp Fermi surface ( points in 1D). It was conjectured [7] that as long as the system is metallic, namely, states are delocalized at the Fermi energy, there will be area law violation.
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