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arXiv:1803.07990 · Physical Review Letters

Diagrammatic Monte Carlo Approach to Angular Momentum in Quantum Many-Particle Systems

Giacomo Bighin, Timur V. Tscherbul, Mikhail Lemeshko

Published Oct 16, 2018• 18 citations
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Abstract

We introduce a diagrammatic Monte Carlo 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.

DOI
10.1103/physrevlett.121.165301

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We introduce a diagrammatic Monte Carlo 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.
We introduce a Diagrammatic Monte Carlo (DiagMC) approach to complex molecular impurities with rotational degrees of freedom interacting with a many-particle environment. The treatment is based on the 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 works 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 quantum impurities possessing angular momentum degrees of freedom.
Feynman diagrams represent one of the most powerful techniques of modern many-particle theory. Applying such diagrammatic techniques to many-body processes involving angular momentum is, however, substantially challenging. Here, the authors introduce a diagrammatic approach to the angulon quasiparticle, which consists of an orbital quantum impurity -- such as a molecule or electron -- exchanging angular momentum with a bath of bosons (superfluid, lattice phonons). The new approach fuses the Feynman diagrams of solid-state physics with the angular momentum diagrams previously used in atomic and nuclear structure calculations.
Diagrammatic Monte Carlo provides a systematically improvable framework for stochastically resumming many-body expansions to high orders through direct sampling of diagram topologies. We advance our earlier work by introducing a novel time-ordered Diagrammatic Monte Carlo algorithm for the single-particle Green's function. The algorithm is tailored to finite nuclei, formulated in discrete model spaces and applicable to arbitrary two-body interactions. The new time-ordered diagrammatic Monte Carlo algorithm is based on the on-the-fly evaluation of time-ordered Goldstone diagrams, avoiding explicit diagram enumeration and expensive frequency integration. We show the algorithm by computing 16{}^{16}16O up to fifth order in a reduced model space using optimized reference state orbitals and including effective three-body forces. Benchmarking against established truncation schemes in ab initio nuclear theory demonstrates its potential to overcome the limitations of current many-body approaches.
We develop a microscopic theory describing a quantum impurity whose rotational degree of freedom is coupled to a many-particle bath. We approach the problem by introducing the concept of an "angulon"-a quantum rotor dressed by a quantum field-and reveal its quasiparticle properties using a combination of variational and diagrammatic techniques. Our theory predicts renormalization of the impurity rotational structure, such as that observed in experiments with molecules in superfluid helium droplets, in terms of a rotational Lamb shift induced by the many-particle environment. Furthermore, we discover a rich many-body-induced fine structure, emerging in rotational spectra due to a redistribution of angular momentum within the quantum many-body system.
Two of the most influential ideas developed by Richard Feynman are the Feynman diagram technique and his variational approach. Here we show that combining both, and introducing a diagrammatic quantum Monte Carlo method, results in a powerful and accurate solver to the generic solid state problem, in which a macroscopic number of electrons interact by the long range Coulomb repulsion. We apply it to the quintessential problem of solid state, the uniform electron gas, which is at the heart of the density functional theory success in describing real materials, yet it has not been adequately solved for over 90 years. Our method allows us to calculate numerically exact momentum and frequency resolved spin and charge response functions. This method can be applied to a number of moderately interacting electron systems, including models of realistic metallic and semiconducting solids.
During the past 70 years, the quantum theory of angular momentum has been successfully applied to describing the properties of nuclei, atoms, and molecules, and their interactions with each other as well as with external fields.Because of the properties of quantum rotations, the angular-momentum algebra can be of tremendous complexity even for a few interacting particles, such as valence electrons of an atom, not to mention larger many-particle systems.In this work, we study an example of the latter: a rotating quantum impurity coupled to a many-body bosonic bath.In the regime of strong impurity-bath couplings, the problem involves the addition of an infinite number of angular momenta, which renders it intractable using currently available techniques.Here, we introduce a novel canonical transformation that allows us to eliminate the complex angular-momentum algebra from such a class of many-body problems.In addition, the transformation exposes the problem's constants of motion, and renders it solvable exactly in the limit of a slowly rotating impurity.We exemplify the technique by showing that there exists a critical rotational speed at which the impurity suddenly acquires one quantum of angular momentum from the many-particle bath.Such an instability is accompanied by the deformation of the phonon density in the frame rotating along with the impurity.