arXiv:0706.1805 · Journal of Mathematical Physics

The von Neumann entropy asymptotics in multidimensional fermionic systems

Szilárd Farkas, Zoltán Zimborás

Published Oct 1, 2007• 33 citations

Abstract

We study the von Neumann entropy asymptotics of pure translation-invariant quasifree states of d-dimensional fermionic systems. It is shown that the entropic area law is violated by all these states: apart from the trivial cases, the entropy of a cubic subsystem with edge length L cannot grow slower than Ld−1lnL. As for the upper bound of the entropy asymptotics, the zero-entropy-density property of these pure states is the only limit: it is proven that arbitrary fast sub-Ld entropy growth is achievable.

DOI: 10.1063/1.2800167

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