QUROPE Quantum Information Processing and Communication in Europe

The quantum information approach to many body physics has been very successful in giving new insight and novel numerical methods. In these lecture notes we take a vertical view of the subject, starting from general concepts and at each step delving into applications or consequences of a particular topic. We first review some general quantum information concepts like entanglement and entanglement measures, which leads us to entanglement area laws. We then continue with one of the most famous examples of area-law abiding states: matrix product states, and tensor product states in general. Of these, we choose one example (classical superposition states) to introduce recent developments on a novel quantum many body approach: quantum kinetic Ising models. We conclude with a brief outlook of the field.