Diagrammatic Monte Carlo approach to angular momentum in quantum many-body systems Main reference: Phys. Rev. Lett. 121 , 165301 (2018). 1 Institute of Science and Technology Austria 2 University of Nevada, Reno DPG Frühjahrstagung, Rostock, March 15th, 2019 G. Bighin 1 , T.V. Tscherbul 2 and M. Lemeshko 1
Quantum impurities One particle (or a few particles) interacting with a many-body environment. Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: , . Image from: F. Chevy, Physics 9 , 86. Composite impurity , e.g. a diatomic molecule: translational and rotational degrees of freedom/linear and angular momentum exchange. 2/11
Quantum impurities One particle (or a few particles) interacting with a many-body environment. Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: electron in a solid, atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity , e.g. a diatomic molecule: translational and rotational degrees of freedom/linear and angular momentum exchange. 2/11
Quantum impurities One particle (or a few particles) interacting with a many-body environment. Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity , e.g. a diatomic molecule: translational and rotational degrees of freedom/linear and angular momentum exchange. 2/11 Most common cases: electron in a solid,
Quantum impurities One particle (or a few particles) interacting with a many-body environment. Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: electron in a solid, atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity , e.g. a diatomic molecule: translational and rotational degrees of freedom/linear and angular momentum exchange. 2/11
Quantum impurities One particle (or a few particles) interacting with a many-body environment. Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: electron in a solid, atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity , e.g. a diatomic molecule: translational and rotational degrees of freedom/linear and angular momentum exchange. 2/11 This scenario can be formalized in terms of quasiparticles using the polaron and the Fröh- lich Hamiltonian.
Quantum impurities One particle (or a few particles) interacting with a many-body environment. Structureless impurity: translational degrees of freedom/linear momentum exchange with the bath. Most common cases: electron in a solid, atomic impurities in a BEC. Image from: F. Chevy, Physics 9 , 86. Composite impurity , e.g. a diatomic molecule: translational and rotational degrees of freedom/linear and angular momentum exchange. 2/11 This scenario can be formalized in terms of quasiparticles using the polaron and the Fröh- lich Hamiltonian.
Quantum impurities quasiparticles using the polaron and the Fröh- Vilesov, Angew. Chem. Int. Ed. 43 , Image from: J. P. Toennies and A. F. Stapelfeldt. Henrik Plenary talk: nanodroplets. helium embedded into Molecules lich Hamiltonian. This scenario can be formalized in terms of One particle (or a few particles) interacting with a many-body environment. 2/11 exchange. freedom/linear and angular momentum translational and rotational degrees of Composite impurity , e.g. a diatomic molecule: Image from: F. Chevy, Physics 9 , 86. atomic impurities in a BEC. Most common cases: electron in a solid, exchange with the bath. degrees of freedom/linear momentum Structureless impurity: translational 2622 (2004).
Quantum impurities 2/11 Lemeshko, Phys. Rev. A 94 , 041601(R) B. Midya, M. Tomza, R. Schmidt, and M. ions. molecules and Ultracold lich Hamiltonian. quasiparticles using the polaron and the Fröh- This scenario can be formalized in terms of exchange. One particle (or a few particles) interacting with a many-body environment. freedom/linear and angular momentum translational and rotational degrees of Composite impurity , e.g. a diatomic molecule: Image from: F. Chevy, Physics 9 , 86. atomic impurities in a BEC. Most common cases: electron in a solid, exchange with the bath. degrees of freedom/linear momentum Structureless impurity: translational (2016).
Quantum impurities This scenario can be formalized in terms of Image from: C. Eames et al, Nat. 214114 (2016). J. Lahnsteiner et al., Phys. Rev. B 94 , T. Chen et al., PNAS 114 , 7519 (2017). perovskites. inside a ‘cage’ in molecules Rotating lich Hamiltonian. quasiparticles using the polaron and the Fröh- 2/11 One particle (or a few particles) interacting with a many-body environment. exchange. freedom/linear and angular momentum translational and rotational degrees of Composite impurity , e.g. a diatomic molecule: Image from: F. Chevy, Physics 9 , 86. atomic impurities in a BEC. Most common cases: electron in a solid, exchange with the bath. degrees of freedom/linear momentum Structureless impurity: translational Comm. 6 , 7497 (2015).
Quantum impurities exchange. 2. Feynman diagrams. 1. A rotating impurity as a quasiparticle. This talk: lich Hamiltonian. quasiparticles using the polaron and the Fröh- This scenario can be formalized in terms of 2/11 freedom/linear and angular momentum One particle (or a few particles) interacting with a many-body environment. translational and rotational degrees of Composite impurity , e.g. a diatomic molecule: Image from: F. Chevy, Physics 9 , 86. atomic impurities in a BEC. Most common cases: electron in a solid, exchange with the bath. degrees of freedom/linear momentum Structureless impurity: translational 3. Diagrammatic Monte Carlo.
The angulon phonons 4 Y. Shchadilova, ”Viewpoint: A New Angle on Quantum Impurities” , Physics 10 , 20 (2017). 3 M. Lemeshko, Phys. Rev. Lett. 118 , 095301 (2017). 2 R. Schmidt and M. Lemeshko, Phys. Rev. X 6 , 011012 (2016). 1 R. Schmidt and M. Lemeshko, Phys. Rev. Lett. 114 , 203001 (2015). bath 3 . molecule in any kind of bosonic • Phenomenological model for a weakly-interacting BEC 1 . • Derived rigorously for a molecule in a • Linear molecule. molecule-phonon interaction A composite, rotating impurity in a bosonic environment can be described by 3/11 J 2 molecule the angulon Hamiltonian 1 , 2 , 3 , 4 (angular momentum basis: k → { k , λ, µ } ): [ ] ∑ ∑ ω k ˆ k λµ ˆ λµ (ˆ θ, ˆ ϕ )ˆ k λµ + Y λµ (ˆ θ, ˆ ϕ )ˆ ˆ B ˆ b † Y ∗ b † H = + + U λ ( k ) b k λµ b k λµ ���� k λµ k λµ � �� � � �� �
The angulon phonons 4 Y. Shchadilova, ”Viewpoint: A New Angle on Quantum Impurities” , Physics 10 , 20 (2017). 3 M. Lemeshko, Phys. Rev. Lett. 118 , 095301 (2017). 2 R. Schmidt and M. Lemeshko, Phys. Rev. X 6 , 011012 (2016). 1 R. Schmidt and M. Lemeshko, Phys. Rev. Lett. 114 , 203001 (2015). part. symmetric part. bath 3 . molecule in any kind of bosonic • Phenomenological model for a weakly-interacting BEC 1 . • Derived rigorously for a molecule in a • Linear molecule. molecule-phonon interaction A composite, rotating impurity in a bosonic environment can be described by 3/11 J 2 molecule the angulon Hamiltonian 1 , 2 , 3 , 4 (angular momentum basis: k → { k , λ, µ } ): [ ] ∑ ∑ ω k ˆ k λµ ˆ λµ (ˆ θ, ˆ ϕ )ˆ k λµ + Y λµ (ˆ θ, ˆ ϕ )ˆ ˆ B ˆ b † Y ∗ b † H = + + U λ ( k ) b k λµ b k λµ ���� k λµ k λµ � �� � � �� � λ = 0: spherically λ ≥ 1 anisotropic
How do we describe molecular rotations with Feynman diagrams? How does Feynman diagrams angular momentum enter this picture? GB and M. Lemeshko, Phys. Rev. B 96 , 419 (2017). 4/11 = + + + + . . .
How do we describe molecular rotations with Feynman diagrams? How does Feynman diagrams angular momentum enter this picture? Fröhlich polaron GB and M. Lemeshko, Phys. Rev. B 96 , 419 (2017). 4/11 = + + + + . . .
How do we describe molecular rotations with Feynman diagrams? How does Feynman diagrams angular momentum enter this picture? Angulon GB and M. Lemeshko, Phys. Rev. B 96 , 419 (2017). 4/11 = + + + + . . .
How do we describe molecular rotations with Feynman diagrams? How does Feynman diagrams angular momentum enter this picture? Angulon Write on each line j,m: angular mo- mentum and pro- jection along z axis. GB and M. Lemeshko, Phys. Rev. B 96 , 419 (2017). 4/11 = + + + + . . .
How do we describe molecular rotations with Feynman diagrams? How does Feynman diagrams angular momentum enter this picture? Angulon Angular momentum- dependent propagators: GB and M. Lemeshko, Phys. Rev. B 96 , 419 (2017). 4/11 = + + + + . . . G 0 , j and D λ
Feynman diagrams j 1 GB and M. Lemeshko, Phys. Rev. B 96 , 419 (2017). m 3 m 2 m 1 j 3 j 2 each vertex: A 3 j symbol for Angulon angular momentum enter this picture? How do we describe molecular rotations with Feynman diagrams? How does 4/11 = + + + + . . . ( )
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