Diff. Geom, Math. Phys., PDE Seminar: Wolfgang Spitzer
- Date: 05/13/2014
- Time: 15:30
University of British Columbia
Scaling of Rényi entanglement entropies of the free Fermi-gas ground state
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.
Location: ESB 4127