Momentum-space quantum information in field theories

Our current understanding of many-body systems and quantum fields is underpinned by two powerful frameworks: the Renormalization Group ideas developed by Wilson, among others, and a more recent approach based on quantum information, pushed forward by works such as those of Wen and Kitaev. In this talk, I will give an overview of recent developments in combining the two perspectives through the study of entanglement between the momentum-space degrees of freedom and the constraints naturally imposed by renormalization. Results include a path-integral method for calculating such entanglement entropies, an equivalence between the Wilsonian RG procedure and a specific quantum channel and the separability of many-body ground states of so-called fixed point theories. Finally, I will briefly discuss how this line of investigation may be taken forward and help with the study of quantum phases of matter.