Mutual information in interacting spin systems

Abstract

This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting spins. Quantum information theory often focuses on the ground state of such systems; we will however be interested in what happens at finite temperature. Using mutual information, which can be seen as a generalization of entanglement entropy to the finite-temperature case, we can study the different phases occurring in these models, and in particular the phase transitions between those. We examine broadly two different classes of models: classical spins on two-dimensional lattices, and fully-connected models of quantum-mechanical spin-1/2 particles. (Abstract abridged.)