Décroissance de l’information mutuelle pour les états de Gibbs des Hamiltoniens locaux. – (Andreas Bluhm / LPT / Seminar). – 23/04/2024, 14 H.

Andreas Bluhm (LIG, Grenoble)

Seminar LPT, 23/04/2024, 14H, 3R1, seminar room, 3rd floor

Abstract :
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 first consider 1D quantum spin systems with local, finite-range, translation-invariant interactions at any temperature. In this setting, we show the mutual information between two regions decays exponentially with their distance, irrespective of the temperature. In higher dimensions, we will show such a decay holds above a critical temperature, assuming the existence of a suitable effective Hamiltonian. The main tool for our analysis will be the expansionals introduced by Araki.