The von Neumann entropy asymptotics in multidimensional fermionic systems

TL;DR

This paper investigates the growth of von Neumann entropy in multidimensional fermionic systems, revealing violations of the entropic area law and demonstrating the potential for rapid entropy growth.

Contribution

It establishes the violation of the entropic area law in pure translation-invariant fermionic states and characterizes the possible entropy growth rates.

Findings

Entropy of cubic subsystems grows at least as L^{d-1}ln L

Pure states can exhibit arbitrarily fast sub-L^d entropy growth

Zero-entropy-density property is the only upper bound for entropy growth

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.