On the Area Law for Disordered Free Fermions

Abstract

We study theoretically and numerically the entanglement entropy of the $d$-dimensional free fermions whose one body Hamiltonian is the Anderson model. Using basic facts of the exponential Anderson localization, we show first that the disorder averaged entanglement entropy $⟨S_{\Lambda }⟩$ of the $d$ dimension cube $\Lambda$ of side length $l$ admits the area law scaling $⟨S_{\Lambda }⟩\sim l^{(d-1)},l\gg 1$ even in the gapless case, thereby manifesting the area law in the mean for our model. For $d=1$ and $l\gg 1$ 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 selfaveraging, i.e., has non vanishing random fluctuations even if $l\gg 1$.

4 pages, 1 figure

References in corpus (4)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Entanglement scaling in critical two-dimensional fermionic and bosonic systems
• Entanglement in fermionic systems
• An Area Law for the Bipartite Entanglement of Disordered Oscillator Systems

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• Entanglement in composite free-fermion systems
• The Widom-Sobolev formula for discontinuous matrix-valued symbols
• Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model
• Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension
• An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator
• Entanglement Entropy of Free Fermions with a Random Matrix as a One-Body Hamiltonian