Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions

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.

arXiv comment4 pages, 4 figures, 3 references added

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• Entanglement scaling of excited states in large one-dimensional many-body localized systems
• Area Law for Gapless States from Local Entanglement Thermodynamics
• Large Block Properties of the Entanglement Entropy of Disordered Fermions
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Entanglement in composite free-fermion systems
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization
• Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model
• Directional Localization in Disordered 2D Tight-Binding Systems: Insights from Single Particle Entanglement Measures
• Anderson localization: a density matrix approach