Abstract
We show that entanglement entropy of free fermions scales faster than area law, as opposed to the scaling for the harmonic lattice, for example. We also suggest and provide evidence in support of an explicit formula for the entanglement entropy of free fermions in any dimension , as the size of a subsystem , where is the Fermi surface and is the boundary of the region in real space. The expression for the constant is based on a conjecture due to Widom. We prove that a similar expression holds for the particle number fluctuations and use it to prove a two sided estimate on the entropy .
- Received 10 May 2005
DOI:https://doi.org/10.1103/PhysRevLett.96.100503
©2006 American Physical Society