Andreas Bluhm

The thermal equilibrium properties of physical systems can be described using Gibbs states. It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between distant regions are small. In this talk, we will start with a short overview of how to quantify correlations in quantum spin systems. Then, we will focus on 1D quantum spin systems (spin chains) with local, finite-range, translation-invariant interactions at any temperature. In this setting, we can show that for Gibbs states, the mutual information between two regions decays exponentially with their distance. Finally, we will consider in how far these results translate to higher dimensions.