Scaling of Rényi entanglement entropies of the free fermi-gas ground state: a rigorous proof

In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Gioev and Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bipartite von Neumann entanglement entropy of noninteracting fermions in multidimensional Euclidean space at zero temperature. Based on recen...

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Bibliographic Details
Published in:Physical review letters 2014-04, Vol.112 (16), p.160403-160403, Article 160403
Main Authors: Leschke, Hajo, Sobolev, Alexander V, Spitzer, Wolfgang
Format: Article
Language:English
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Summary:In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Gioev and Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bipartite von Neumann entanglement entropy of noninteracting fermions in multidimensional Euclidean space at zero temperature. Based on recent progress by one of us (A. V. S.) in semiclassical functional calculus for pseudodifferential operators with discontinuous symbols, we provide here a complete proof of that formula and of its generalization to Rényi entropies of all orders α>0. The special case α=1/2 is also known under the name logarithmic negativity and often considered to be a particularly useful quantification of entanglement. These formulas exhibiting a "logarithmically enhanced area law" have been used already in many publications.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.112.160403