Diagrammatic Monte Carlo

Mathematically speaking, Diagrammatic Monte Carlo (DiagMC) is a generalization of Metropolis-Hastings algorithm used for sampling series of similar integrals with variable number of integration variables. Feynman diagrams is the most typical and important but still not the only example of series that can be sampled with DiagMC. I will start with introducing general principles of DiagMC and then present illustrative applications to paradigmatic condensed matter models: resonant fermions, uniform electron gas, Hubbard model, spins lattices, impurity models, and various types of polarons.