Diagrammatic Monte Carlo approach to rotating molecular impurities

We introduce a Diagrammatic Monte Carlo (DiagMC) approach to complex molecular impurities with rotational degrees of freedom interacting with a many-particle environment. The treatment is based on the diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach works at arbitrary coupling, is free of systematic errors and of finite size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model, however, the method is quite general and can be applied to a broad variety of quantum impurities possessing angular momentum degrees of freedom.