Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment Journal Article

Author(s): Bighin, Giacomo; Lemeshko, Mikhail
Article Title: Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment
Affiliation IST Austria
Abstract: Recently it was shown that an impurity exchanging orbital angular momentum with a surrounding bath can be described in terms of the angulon quasiparticle [Phys. Rev. Lett. 118, 095301 (2017)]. The angulon consists of a quantum rotor dressed by a many-particle field of boson excitations, and can be formed out of, for example, a molecule or a nonspherical atom in superfluid helium, or out of an electron coupled to lattice phonons or a Bose condensate. Here we develop an approach to the angulon based on the path-integral formalism, which sets the ground for a systematic, perturbative treatment of the angulon problem. The resulting perturbation series can be interpreted in terms of Feynman diagrams, from which, in turn, one can derive a set of diagrammatic rules. These rules extend the machinery of the graphical theory of angular momentum - well known from theoretical atomic spectroscopy - to the case where an environment with an infinite number of degrees of freedom is present. In particular, we show that each diagram can be interpreted as a 'skeleton', which enforces angular momentum conservation, dressed by an additional many-body contribution. This connection between the angulon theory and the graphical theory of angular momentum is particularly important as it allows to systematically and substantially simplify the analytical representation of each diagram. In order to exemplify the technique, we calculate the 1- and 2-loop contributions to the angulon self-energy, the spectral function, and the quasiparticle weight. The diagrammatic theory we develop paves the way to investigate next-to-leading order quantities in a more compact way compared to the variational approaches.
Keywords: Quantum gases; Atomic Physics; Mesoscale and Nanoscale Physics; Chemical Physics; Other Condensed Matter
Journal Title: Physical Review B - Condensed Matter and Materials Physics
Volume: 96
Issue 8
ISSN: 1550-235X
Publisher: American Physical Society  
Date Published: 2017-08-07
Start Page: Article number: 085410
Sponsor: This work was supported by the Austrian Science Fund (FWF), Project No. P29902-N27.
DOI: 10.1103/PhysRevB.96.085410
Notes: We thank W. Casteels, B. Midya, W. Rzadkowski, R. Schmidt, and E. Yakaboylu, for valuable comments and suggestions at various stages of this work.
Open access: yes (repository)