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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
Published on: September 5, 2019
Entanglement entropy of fermions in any dimension and the Widom conjecture
1Courant Institute, New York University, New York, New York 10012, USA. gioev@math.rochester.edu
Abstract:
We show that entanglement entropy of free fermions scales faster than area law, as opposed to the scaling L(d-1) 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 d, S approximately c(deltagamma, deltaomega)L(d-1) logL as the size of a subsystem L-->infinity, where deltagamma is the Fermi surface and is the boundary of the region in real space. The expression for the constant c(deltagamma, deltaomega) 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 S.
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