Quantum embedding methods, such as dynamical mean-field theory (DMFT) and density matrix embedding theory (DMET) are important methods for treating strongly-correlated quantum materials. Surprisingly, in many scenarios the computational bottleneck is not (just due) to the quantum impurity problem (a quantum many-body problem), but at the single-particle level. For instance, DMFT has the bath fitting problem, and DMET has the correlation potential fitting problem. This tutorial talk will define such problems, and briefly mention some recent ideas for tackling such problems using convex optimization.
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