Entanglement in 'Dirty' Quantum Magnets

Studying quantum entanglement over the past decade has allowed us to make remarkable theoretical progress in understanding correlated many-body quantum systems. However in real materials electrons experience spatially random heterogeneities ("dirt") whose theoretical treatment, including strong correlations, has been a challenge. I will describe how synthesizing ideas from quantum information theory, statistical mechanics, and quantum field theory gives us new insights into the role of randomness in 2D correlated quantum spin ("qubit") systems, enabling us to understand a broad variety of experimental observations. I will also describe how these results lead us to conjectures of general UV-to-IR constraints ("Lieb-Schultz-Mattis") on all possible behaviors of quantum magnets, even with randomness; and further to our current research on disordered topological insulators with anomalous boundary localization, as well as other novel quantum phases across connecting magnetic insulators to metals.