Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

Abstract

The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.

arXiv comment21 pages, 1 figure

References in corpus (27)

• Phonons and related properties of extended systems from density-functional perturbation theory
• The GW method
• Electron-phonon interactions from first principles
• Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures
• Born-Oppenheimer Breakdown in Graphene
• Exact factorization of the time-dependent electron-nuclear wavefunction
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Quantum Crystal Structure in the 250 K Superconducting Lanthanum Hydride
• Thermal properties of materials from ab-initio quasi-harmonic phonons
• Fully selfconsistent GW calculations for molecules
• Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction
• Quartic Anharmonicity of Rattlers and Its Effect on Lattice Thermal Conductivity of Clathrates from First Principles
• Levels of self-consistency in the GW approximation
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• Anharmonic phonon spectra of PbTe and SnTe in the self-consistent harmonic approximation
• Exact factorization-based density functional theory of electrons and nuclei
• On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation
• Ab initio study on lattice thermal conductivity of Cu${}_2$O using GGA and hybrid density functional methods
• The Implicit and the Inverse Function theorems: easy proofs
• Approximations for many-body Green's functions: insights from the fundamental equations
• Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF
• Ab initio lattice dynamical studies of silicon clathrate frameworks and their negative thermal expansion
• Exact factorization-based density functional theory of electron-phonon systems
• Ab initio studies on the lattice thermal conductivity of silicon clathrate frameworks II and VIII
• A functional approach to the electronic and bosonic dynamics of many-body systems perturbed with an arbitrary strong electron-boson interaction
• Partial self-consistency and analyticity in many-body perturbation theory: particle number conservation and a generalized sum rule
• Ab initio computational study on the lattice thermal conductivity of Zintl clathrates [Si${}_{19}$P${}_4$]Cl${}_4$ and Na${}_4$[Al${}_4$Si${}_{19}$]

Cited by in corpus (13)

• Towards high-throughput superconductor discovery via machine learning
• Quantum Proton Effects from Density Matrix Renormalization Group Calculations
• Dynamical renormalization of electron-phonon coupling in conventional superconductors
• Exact factorization of the many-body Green's function theory of electrons and nuclei
• Quantifying errors of the electron-proton/muon correlation functionals through the Kohn-Sham inversion of a two-component model system
• Quantum Field Theory of Electrons and Nuclei
• Deep-learning design of graphene metasurfaces for quantum control and Dirac electron holography
• Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data
• Gor'kov-Hedin-Baym Equations for Quantum Many-Body Systems with Spin-Dependent Interactions
• Giant Kohn anomaly and chiral phonons in the charge density wave phase of 1H-NbSe${}_2$
• On the breakdown of the Born-Oppenheimer approximation in LiH and LiD
• Beyond Born-Oppenheimer Green's function theories: absolute and relational
• On the diagonalization of quadratic Hamiltonians