Entanglement Matters: from Bell states to Quantum Tensor Networks

The theory of quantum entanglement is revolutionizing the field of quantum many body physics. One of the most relevant developments in this direction has been the introduction of quantum tensor networks, which provide a natural framework for describing the entanglement structure in ground states of strongly correlated systems. I will give an overview of this new research direction, and discuss applications in the field of low dimensional quantum many body systems, in systems exhibiting topological quantum order, and in simulating gauge field theories.