| Abstract: | 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.
First I will outline our results in two theoretically controlled settings, showing that even weak randomness necessarily nucleates certain topological defects with free spins that control observable physics. Second I will describe how the theory predicts a scaling collapse of the temperature and magnetic-field dependence of the heat capacity that is consistent with experimental observations from multiple materials, suggesting that mild randomness in these materials leads them to exhibit usable long-range entanglement of electron pairs. Third I will describe how these results lead us to conjectures and a 1D proof of general constraints ("Lieb-Schultz-Mattis theorems") on all possible behavior of quantum magnets, even with randomness. This surprising connection is enabling our current research on interacting disordered topological insulators (with "anomalous localization") and promises further applications to entanglement in quantum information devices and topological materials. |