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Q: Fachverband Quantenoptik und Photonik

Q 67: Quantum information: Concepts and methods V

Q 67.2: Vortrag

Freitag, 22. März 2013, 14:15–14:30, E 214

Area Laws for thermal free fermions — •Michael Kastoryano¹, Jens Eisert¹, and Holger Bernigau² — ¹FU Berlin — ²MPI für Mathematik, Leipzig

We introduce a framework allowing to compute the mutual information, showing an area law, as well as the complete spectra of reduced states of translationally invariant free fermionic lattice systems in Gibbs states in a rigorous and asymptoti- cally exact fashion. The framework introduced develops new methods for computing determinants of Toeplitz operators with smooth symbols, and allows for considering Toeplitz matrices the entries of which depend on the physical system size. The expres- sions derived constitute a setting for studying the interplay of ground state scaling of entanglement entropies and temperature effects, showing that only at extremely low temperatures, signatures of criticality can be seen. As an example, we discuss the sit- uations of the XX in one dimension and free fermionic models on the torus in higher dimensions in detail. We highlight in particular the dependence of the mutual informa- tion scaling like the logarithm of the inverse temperature, constituting an exponential improvement over known general bounds derived from the extremality of the free en- ergy.