Relatore: Simone Notarnicola (Università di Padova)
We show recent ansätze and applications based on Tensor Networks (TNs) for the study of quantum many-body systems. We first introduce the general idea of TNs and then we show some of the most recent applications, focusing in particular on the Tree Tensor Network (TTN) ansatz. We show that, on one hand, they can be applied for the study of isolated systems at unprecedented system sizes and at high spatial dimensions. On the other side, we show that the geometry of a TTN offers a natural application in the representation of density matrices for describing open quantum systems. Both these applications make the TNs approach an ideal candidate for classical benchmarking of near-future quantum computers.