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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations

On the Area Law for Disordered Free Fermions

arXiv
Authors: L. Pastur, V. Slavin

Year

2014

Paper ID

48108

Status

Preprint

Abstract Read

~2 min

Abstract Words

122

Citations

N/A

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 langle S_Λrangle of the d dimension cube Λ of side length l admits the area law scaling langle S_Λrangle 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 lgg 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.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We study theoretically and numerically the entanglement entropy of the d-dimensional free fermions whose one body Hamiltonian is the Anderson model.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1408.2570 [2] arXiv https://arxiv.org/abs/1408.2570 [3] Publisher https://arxiv.org/abs/1408.2570

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