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

- Date: 09/29/2015
- Time: 15:30

*Fernuniversitat Hagen*

University of British Columbia

Area Law for the Entanglement Entropy of the Free Fermi Gas at Nonzero Temperature

The leading asymptotic large-scale behavior of the spatially bipartite entanglement entropy (EE) of the free Fermi gas at temperature $T=0$ is by now well understood. Here, we present and discuss the first rigorous results for the corresponding EE of thermal equilibrium states at $T>0$. The leading large-scale term of this thermal EE turns out to be twice the first finite-size correction to the infinite-volume thermal entropy (density). However, it is given by a rather complicated integral derived from semiclassical trace formulas and differs, at least at high temperature, from simpler expressions previously obtained by arguments based on a conformal field theory. In the zero-temperature limit, the leading large-scale term of the thermal EE considerably simplifies and displays a $\ln(1/T)$-singularity which one may identify with the known logarithmic correction at $T=0$ to the so-called area-law scaling. This is joint work with Hajo Leschke and Alexander Sobolev.

Location: ESB 2012