Abstract

Free fermion systems enjoy a privileged place in physics. With their simple structure they can explain a wide variety of effects, ranging from insulating and metallic behaviour to superconductivity and the integer quantum Hall effect. All their quantum properties can be derived by a small set of data that scales linearly with the system size. Interactions, e.g. in the form of Coulomb repulsion, can dramatically alter this picture giving rise to emerging physics that have no resemblance to free fermions. Within that realm physical effects such as high-temperature superconductivity, fractional quantum Hall effect, Kondo effect are met with the promise of a wide range of technological applications. Nevertheless, the study of interacting systems is recognised as one of the hardest problems in physics due to the lack of a systematic approaches in solving them. In this talk I will present a general framework to study the manifestations of interacting systems. The aim is to use quantum information tools to quantify the effect of interactions and to identify the optimal Gaussian states that best approximate their eigenstates.