• entanglement entropy
• entanglement asymmetry
• conformal field theory

Entanglement entropy has proved to be a vital tool for understanding many phenomena in quantum many-body physics. It provides one of the most convenient ways to measure entanglement, which in turn is one of the most fundamental properties of quantum systems. The aim of this work is not simply that of studying entanglement entropy in itself: we wish to study how this fundamental quantity relates to symmetries. In particular our focus will be that of studying the "entanglement asymmetry" ­– a quantity that has been introduced recently in this context; we develop a suitable description of entanglement asymmetry within the framework of quantum field theory, and we use it to study systems that break a non-abelian SU(2) symmetry. The particular field theory that we consider for the concrete calculations is an effective description of the critical phase of a 1d spin model – the XXZ model. We also resort to numerical simulations of this model to analyze the behaviour of the lattice system and compare it to the field-theoretical results.