The von Neumann entropy asymptotics in multidimensional fermionic systems
Mathematical Physics
2011-05-09 v2 Statistical Mechanics
math.MP
Quantum Physics
Abstract
We study the von Neumann entropy asymptotics of pure translation-invariant quasi-free 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 L^{d-1}ln L. 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-L^d entropy growth is achievable.
Cite
@article{arxiv.0706.1805,
title = {The von Neumann entropy asymptotics in multidimensional fermionic systems},
author = {S. Farkas and Z. Zimboras},
journal= {arXiv preprint arXiv:0706.1805},
year = {2011}
}