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

Diagrammatic approach to orbital quantum impurities interacting with a many-particle environment 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)10.1103/PhysRevLett.118.095301]. 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 us to systematically and substantially simplify the analytical representation of each diagram. In order to exemplify the technique, we calculate the one- and two-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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

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

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

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)10.1103/PhysRevLett.118.095301]. 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 us to systematically and substantially simplify the analytical representation of each diagram. In order to exemplify the technique, we calculate the one- and two-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.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1098-0121
eISSN
1550-235X
D.O.I.
10.1103/PhysRevB.96.085410
Publisher site
See Article on Publisher Site

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)10.1103/PhysRevLett.118.095301]. 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 us to systematically and substantially simplify the analytical representation of each diagram. In order to exemplify the technique, we calculate the one- and two-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.

Journal

Physical Review BAmerican Physical Society (APS)

Published: Aug 7, 2017

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