Diff. Geom, Math. Phys., PDE Seminar: Wolfgang Spitzer

In the remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Dimitri Gioev and Israel Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bi-partite von-Neumann entanglement entropy of non-interacting fermions in multi-dimensional Euclidean space at zero temperature. Based on recent progress by one of us (A.V.S.) in semi-classical functional calculus for pseudo-differential operators with discontinuous symbols, we provide here a complete proof of that formula and of its generalization to Rényi entropies of all orders $\alpha>0$. The special case $\alpha=1/2$ is also known under the name logarithmic negativity and often considered to be a particularly useful quantification of entanglement. These formulas, exhibiting a “logarithmically enhanced area law,” have been used already in many publications.  

This is joint work with Hajo Leschke and Alexander V. Sobolev which will be published in Phys. Rev. Lett.