  We introduce a Diagrammatic Monte Carlo (DiagMC) approach to angular momentum
properties of quantum many-particle systems possessing a macroscopic number of
degrees of freedom. The treatment is based on a 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 is applicable 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 systems in
which particles exchange quantum angular momentum with their many-body
environment.
