Anomalous propagators and the particle-particle channel: Hedin's equations

Abstract

Hedin's equations provide an elegant route to compute the exact one-body Green's function (or propagator) via the self-consistent iteration of a set of non-linear equations. Its first-order approximation, known as $GW$, corresponds to a resummation of ring diagrams and has shown to be extremely successful in physics and chemistry. Systematic improvement is possible, although challenging, via the introduction of vertex corrections. Considering anomalous propagators and an external pairing potential, we derive a new self-consistent set of closed equations equivalent to the famous Hedin equations but having as a first-order approximation the particle-particle (pp) $T$-matrix approximation where one performs a resummation of the ladder diagrams. This pp version of Hedin's equations offers a way to go systematically beyond the $T$-matrix approximation by accounting for low-order pp vertex corrections.

arXiv comment12 pages, 5 figures (Supp. Mat. available)

References in corpus (63)

• BCS-BEC Crossover: From High Temperature Superconductors to Ultracold Superfluids
• Pairing in nuclear systems: from neutron stars to finite nuclei
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Ab-initio theory of superconductivity - I: Density functional formalism and approximate functionals
• The Ground State Correlation Energy of the Random Phase Approximation from a Ring Coupled Cluster Doubles Approach
• Ab-initio theory of superconductivity - II: Applications to elemental metals
• Fully selfconsistent GW calculations for molecules
• Generalized Hartree-Fock Theory and the Hubbard Model
• Pseudogap and spectral function from superconducting fluctuations to the bosonic limit
• Strong-coupling theory of superconductivity in a degenerate Hubbard model
• High Accuracy Many-Body Calculational Approaches for Excitations in Molecules
• Projected Quasiparticle Theory for Molecular Electronic Structure
• Ab-initio Gorkov-Green's function calculations of open-shell nuclei
• Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• Electronic structure and magnetic properties of correlated metals: A local self-consistent perturbation scheme
• Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory
• LDA++ approach to electronic structure of magnets: correlation effects in iron
• Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random Phase Approximation
• Beyond the GW approximation: combining correlation channels
• Strong correlations via constrained-pairing mean-field theory
• All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules
• Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - II. Numerical implementation at second order with a two-nucleon interaction
• Self-consistent Green's function theory for atomic nuclei
• Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Spin-dependent Hedin's equations
• Equivalence of Particle-Particle Random Phase Approximation Correlation Energy and Ladder-Coupled-Cluster-Double
• Faddeev description of two-hole one-particle motion and the single-particle spectral function
• Quantitative Molecular Orbital Energies within a $G_0{W}_0$ Approximation
• In medium T-matrix for nuclear matter with three-body forces - binding energy and single particle properties
• FLEX+DMFT approach to the $d$-wave superconducting phase diagram of the two-dimensional Hubbard model
• Connections and performances of Green's function methods for charged and neutral excitations
• Electron-magnon scattering in elementary ferromagnets from first principles: lifetime broadening and band anomalies
• Fermi gas throughout the BCS-BEC crossover: Comparative study of t-matrix approaches with various degrees of self-consistency
• Quasiparticles in Neon using the Faddeev Random Phase Approximation
• Self-consistent solution of Galitskii-Feynman equations at finite temperature
• Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules
• Tiling with triangles: parquet and $GW\gamma$ methods unified
• Self-consistency in $GW\Gamma$ formalism leading to quasiparticle-quasiparticle couplings
• Entanglement between pairing and screening in the Gorkov-Melik-Barkhudarov correction to the critical temperature throughout the BCS-BEC crossover
• Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems
• Are multi-quasiparticle interactions important in molecular ionization?
• Renormalized Singles Green's Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation
• Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs
• Reference Energies for Valence Ionizations and Satellite Transitions
• Moving away from singly-magic nuclei with Gorkov Green's function theory
• The three channels of many-body perturbation theory: $GW$, particle-particle, and electron-hole $T$-matrix self-energies
• The mathematics of functional differentiation under conservation constraint
• Total energies from variational functionals of the Green function and the renormalized four-point vertex
• Constrained-Pairing Mean-Field Theory. IV. Inclusion of corresponding pair constraints and connection to unrestricted Hartree-Fock theory
• Linear Scaling Calculations of Excitation Energies with Active-Space Particle-Particle Random Phase Approximation
• Projected Quasi-particle Perturbation theory
• Faddeev Random Phase Approximation for Molecules
• Gorkov algebraic diagrammatic construction formalism at third order
• In medium T-matrix for superfluid nuclear matter
• Diagrammatic calculation of thermodynamical quantities in nuclear matter
• BCS-BEC Crossover and Pairing Fluctuations in a Two Band Superfluid/Superconductor: A T Matrix Approach
• Conserving T-matrix theory of superconductivity
• Embedding vertex corrections in GW self-energy: theory, implementation, and outlook
• Importance truncation in non-perturbative many-body techniques
• Influence of impurities on electronic structure in cuprate superconductors

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• Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation
• Double Ionization Potential Equation-of-Motion Coupled-Cluster Approach with Full Inclusion of 4-Hole-2-Particle Excitations and Three-Body Clusters
• Accurate and Efficient Prediction of Double Excitation Energies Using the Particle-Particle Random Phase Approximation
• Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment
• Complex Absorbing Potential Green's Function Methods for Resonances
• Parquet theory for molecular systems: Formalism and static kernel parquet approximation
• Gor'kov-Hedin-Baym Equations for Quantum Many-Body Systems with Spin-Dependent Interactions
• LibppRPA: An Open-Source Library for Particle-Particle Random Phase Approximation