The angulon quasiparticle [1], formalizing the concept of a composite, rotating impurity in a quantum many-body environment, has proven useful in the description of several experimental settings, including cold molecules in a Bose-Einstein condensate or embedded in helium nanodroplets, electronic excitations in a BEC or in a solid.

Building upon this quasiparticle description, we introduce a Diagrammatic Monte Carlo (DiagMC) approach to complex molecular impurities, possessing rotational degrees of freedom [2]. The technique is based on a diagrammatic expansion [3] 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. As a result of the peculiar way in which angular momenta couple, the configuration space is larger with respect to most Diagrammatic Monte Carlo applications, and a new class of updates is needed in order to span it completely.

We exemplify the technique by obtaining an all-coupling solution of the angulon model, showing that our approach correctly recovers the strong-coupling limit, while also naturally providing access to the impurity Green function. However, the technique is general and can be applied to a broad variety of quantum impurities possessing angular momentum degrees of freedom, thereby establishing a connection between DiagMC techniques and molecular simulations.

[1] M. Lemeshko and R. Schmidt, “Molecular impurities interacting with a many-particle environment: from ultracold gases to helium nanodroplets” in “Cold Chemistry: Molecular Scattering and Reactivity Near Absolute Zero”, eds. O. Dulieu and A. Osterwalder (2017), arXiv:1703.06753.

[2] G. Bighin, T. V. Tscherbul, M. Lemeshko, arXiv:1803.07990

[3] G. Bighin and M. Lemeshko, Phys. Rev. B 96, 419 (2017).