Entanglement Measures in Quantum Field Theory

This talk lies at the interface between field theory and foundations of quantum mechanics. I will be speaking about a quintessential quantum mechanical phenomenon, entanglement, mostly in the context of quantum field theory in 1+1D. In this setting, I will introduce some of the most studied bipartite entanglement measures that are investigated in the context of many-body quantum physics: entanglement entropy, Rényi entropies, logarithmic negativity and symmetry-resolved measures. I will explain what the study of entanglement measures signifies within quantum field theory, especially how such measures are effective probes for a wide range of universal properties from identifying critical points and gapped phases to classifying quantum states according to area or volume laws, quantifying the speed of thermalization after a quantum quench, or identifying symmetries and their breaking. I will illustrate some of these points with results from my own work of the past 20 years, particularly the branch point twist field technique that I co-pioneered with J. L. Cardy and B. Doyon in our paper https://arxiv.org/abs/0706.3384. This method relates all measures of entanglement mentioned above to correlation functions of local fields and has enabled us to apply known techniques to compute correlators to the investigation of entanglement measures. Also see the recent review https://arxiv.org/abs/2403.06652.