The GW method

Abstract

Calculations of ground-state and excited-state properties of materials have been one of the major goals of condensed matter physics. Ground-state properties of solids have been extensively investigated for several decades within the standard density functional theory. Excited state properties, on the other hand, were relatively unexplored in ab initio calculations until a decade ago. The most suitable approach up to now for studying excited-state properties of extended systems is the Green function method. To calculate the Green function one requires the self-energy operator which is non-local and energy dependent. In this article we describe the GW approximation which has turned out to be a fruitful approximation to the self-energy. The Green function theory, numerical methods for carrying out the self-energy calculations, simplified schemes, and applications to various systems are described. Self-consistency issue and new developments beyond the GW approximation are also discussed as well as the success and shortcomings of the GW approximation.

75 pages, latex2e, 21 eps figure, additional material avalable at http://www.mpi-stuttgart.mpg.de/docs/ANDERSEN/gw/

References in corpus (2)

• On-site correlation in valence and core states of ferromagnetic nickel
• Electron self-energy in A3C60 (A=K, Rb): Effects of t1u plasmon in GW approximation

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• Two-Particle Self-Consistent method for the multi-orbital Hubbard model
• Frontier molecular orbitals of single molecules adsorbed on thin insulating films supported by a metal substrate: A simplified density functional theory approach
• Image effects in transport at metal-molecule interfaces
• Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory
• Spatial Control of Multiphoton Electron Excitations in InAs Nanowires by Varying Crystal Phase and Light Polarization
• Exact-Exchange Kohn-Sham formalism applied to one-dimensional periodic electronic systems
• Dyson Orbitals, Quasi-Particle effects and Compton scattering
• Ab-initio approach for gap plasmonics
• Extended regime of coexisting metallic and insulating phases in a two-orbital electronic system
• Low Rank Approximation in $G_0{W}_0$ Approximation
• Universal polarization energies for defects in monolayer, surface and bulk hexagonal boron nitride : A finite-size fragments GW approach
• Towards Photoferroic Materials by Design: Recent Progresses and Perspective
• Conductance and polarization in quantum junctions
• Can $GW$ Handle Multireference Systems?
• Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections
• Coulomb interactions and conventional superconductivity: when going beyond the random phase approximation is essential
• Large anomalous Nernst coefficient in an oxide Skyrmion crystal Chern insulator
• Vertex effects in describing the ionization energies of the first-row transition-metal monoxide molecules
• First-principles method to study near-field radiative heat transfer
• Nonuniform grids for Brillouin zone integration and interpolation
• $GW$ study of pressure-induced topological insulator transition in group IV-tellurides
• Anomalous molecular orbital variation upon adsorption on wide band gap insulator
• Probing the LDA-1/2 method as a starting point for $G_0{W}_0$ calculations
• Partial self-consistency and analyticity in many-body perturbation theory: particle number conservation and a generalized sum rule
• Peak Broadening in Photoelectron Spectroscopy of Amorphous Polymers: the Leading Role of the Electrostatic Landscape
• Systematic strain-induced bandgap tuning in binary III-V semiconductors from density functional theory
• Lifetimes of Shockley electrons and holes at the Cu(111) surface
• Ab initio model of amorphous zinc oxide (a-ZnO) and a-X_0.375 Z_0.625 O (X=Al, Ga and In)
• Potassium-intercalated bulk HfS${}_2$ and HfSe${}_2$: Phase stability, structure, and electronic structure
• Modeling the electronic structure of organic materials: A solid-state physicist's perspective
• Effect of Hubbard U on the construction of low energy Hamiltonians for LaMnO_3 via maximally localized Wannier functions
• Mean-field approximation for thermodynamic and spectral functions of correlated electrons: Strong-coupling and arbitrary band filling
• Towards temperature-induced topological phase transition in SnTe: A first principles study
• On the ab initio calculation of CVV Auger spectra in closed-shell systems
• Image-potential band-gap narrowing at a metal/semiconductor interface
• Anisotropy of electronic correlations: On the applicability of local theories to layered materials
• LIBAMI: Implementation of Algorithmic Matsubara Integration
• Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency
• Dielectric function and thermodynamic properties of jellium in the GW approximation
• Challenges with relativistic GW calculations in solids and molecules
• Ab initio investigation on the experimental observation of metallic hydrogen
• Correlated excited states in the narrow gap band semiconductor FeSi and antiferromagnetic screening of local spin moments
• Vibrational and dielectric properties of monolayer transition metal dichalcogenides
• Tunable band gap in twisted bilayer graphene
• Many-body approach to infinite non-periodic systems: application to the surface of semi-infinite jellium
• Identifying Topological Superconductivity in 2D Transition-Metal Dichalcogenides
• Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling
• Accurate ionization potential of gold anionic clusters from density functional theory and many-body perturbation theory
• Coherent Modulation of Quasiparticle Scattering Rates in a Photoexcited Charge-Density-Wave System
• Local Self-Energies for V and Pd Emergent from a Non-Local LDA+FLEX Implementation
• Accurate and efficient prediction of the band gaps and optical spectra of chalcopyrite semiconductors from a non-empirical range-separated dielectric-dependent hybrid: Comparison with many-body perturbation theory
• Unraveling the degradation mechanism of FIrpic based blue OLEDs: I. A theoretical investigation
• Surface-plasmon properties of noble metals with exotic phases
• Modeling X-ray Photoelectron Spectroscopy of Macromolecules Using GW
• Formation of a Te-Ag Honeycomb Alloy: A New Type of Two-Dimensional Material
• Counting Feynman diagrams via many-body relations
• Dielectric screening in extended systems using the self-consistent Sternheimer equation and localized basis sets
• Scalable GW software for quasiparticle properties using OpenAtom
• Description of quasiparticle and satellite properties via cumulant expansions of the retarded one-particle Green's function
• Symmetry Breaking in Occupation Number Based Slave-Particle Methods
• Exact and many-body perturbation solutions of the Hubbard model applied to linear chains
• Interaction created effective flat bands in conducting polymers
• Stochastic pole expansion method
• Nonconvergence of the Feynman-Dyson diagrammatic perturbation expansion of propagators
• Higher Ionization Energies of Atoms in Density Functional Theory
• Self-consistent local GW method: Application to 3d and 4d metals
• Mott metal-insulator transition from steady-state density functional theory
• Causal versus local $GW$+EDMFT scheme and application to the triangular-lattice extended Hubbard model
• Anomalous scaling at non-thermal fixed points of the sine-Gordon model
• A unified Green's function approach for spectral and thermodynamic properties from algorithmic inversion of dynamical potentials
• Optical spectra of 2D monolayers from time-dependent density functional theory
• Phonons, Phase Transitions and Thermal Expansion in LiAlO2: An ab-initio Density Functional Study
• Correlations Between Conduction Electrons in Dense Plasmas
• Non-local correlation effects due to virtual spin-flip processes in itinerant electron ferromagnets
• A spin-polarized scheme for obtaining quasi-particle energies within the density functional theory
• Single-particle spectral function for the classical one-component plasma
• Metric-driven search for structurally stable inorganic compounds
• Fluctuating local field approach to free energy of 1D molecules with strong collective electronic correlations
• Ab-initio calculation of optical absorption in semiconductors: A density-matrix description
• Minimum tracking linear response Hubbard and Hund corrected Density Functional Theory in CP2K
• Combining Density Functional Theory and Green's Function Theory: Range-Separated, Non-local, Dynamic, and Orbital-Dependent Hybrid Functional
• Octave-spanning 1 emission across the visible spectrum from single crystalline 1,3,5,7-tetrakis-($p$-methoxyphenyl)adamantane
• Ab initio simulation of photoemission spectroscopy in solids: Plane-wave pseudopotential approach, with applications to normal-emission spectra of Cu(001) and Cu(111)
• Embedding vertex corrections in GW self-energy: theory, implementation, and outlook
• $GW$ self-screening error and its correction using a local density functional
• Femtosecond dynamics of correlated many-body states in C${}_{60}$ fullerenes
• Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions
• Exploring Coupled Cluster Green's function as a method for treating system and environment in Green's function embedding methods
• Revisiting the homogeneous electron gas in pursuit of the properly normed ab initio Eliashberg theory
• Foundations of the Variational Discrete Action Theory
• Optimized Effective Potential for Extended Hubbard Model
• Comprehensive study on band-gap variations in $s{p}^3$-bonded semiconductors: roles of electronic states floating in internal space
• $\text{Ab initio}$ dynamical mean-field theory with natural orbitals renormalization group impurity solver: Formalism and applications
• Green function theory of orbital magnetic moment of interacting electrons in solids
• Self-energy and lifetime of Shockley and image states on Cu(100) and Cu(111): Beyond the GW approximation of many-body theory
• Helical Organic and Inorganic Polymers
• Spatial Decay and Limits of Quantum Solute-Solvent Interactions
• Many-body $GW$ calculations with very large scale polarizable environments made affordable: a fully ab initio QM/QM approach
• First-principles study of excitons in the optical spectra of silver chloride
• Accurate modeling of FeSe with screened Fock exchange and Hund's metal correlations
• Zero temperature dynamics of the Hubbard model in infinite dimensions: A local moment approach
• Bilayer graphene spectral function in RPA and self-consistent GW
• Accuracy of the Faddeev Random Phase Approximation for Light Atoms
• Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• The Electronic Correlation Strength of Pu
• Plasmonic performance of Au${}_{\mathbf{x}}$Ag${}_{\mathbf{y}}$Cu${}_{1-\mathbf{x}-\mathbf{y}}$ alloys from many-body perturbation theory
• Scaling properties of the Anderson model in the Kondo regime studied by $\sigma G\sigma W$ formalism
• Fermi-Liquid $T^2$ Resistivity: Dynamical Mean-Field Theory Meets Experiment
• Interlayer and intralayer excitons in AlN/WS${}_2$ heterostructure
• LinReTraCe: The Linear Response Transport Centre
• Plasmonic Waveguides from Coulomb-Engineered Two-Dimensional Metals
• Semi-empirical many-body formalism of optical absorption in nanosystems and molecules
• The structure of Green functions in quantum field theory with a general state
• GW with hybrid functionals for large molecular systems
• $G_0{W}_0$ Ionization Potentials of First-Row Transition Metal Aqua Ions
• Fermi-Surface Modeling of Light-Rare-Earth Hexaborides with 2D-ACAR Spectroscopy
• Quasiparticle electronic band structure of the alkali metal chalcogenides
• Optimized Effective Potential Model for the Double Perovskites Sr2-xYxVMoO6 and Sr2-xYxVTcO6
• Spectral functions of the half-filled 1D Hubbard chain within the exchange-correlation potential formalism
• A complementary screening for quantum spin Hall insulators in 2D exfoliable materials
• Strong anisotropic optical properties of 8-Pmmn borophene: a many-body perturbation study
• Electron-Electron Interactions in Device Simulation via Non-equilibrium Green's Functions and the GW Approximation
• Pressure Dependence of Electronic, Vibrational and Optical Properties of wurtzite-Boron Nitride
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Discrete Lehmann representation of three-point functions
• Charge conserving approximation for excitation properties of crystalline materials
• Electronic structure tuning via surface modification in semimetallic nanowires
• Modified $GW$ Method in Electronic Systems
• A QM/MM equation-of-motion coupled-cluster approach for predicting semiconductor color-center structure and emission frequencies
• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• On the interpretation of spin-polarized electron energy loss spectra
• Automated computational workflows for muon spin spectroscopy
• Local vertex corrections from exchange-correlation kernels with a discontinuity
• Optimized correlations inspired by perturbation theory
• Barycentric rational function approximation made simple: A fast analytic continuation method for Matsubara Green's functions
• Role of the Ward Identity and Relevance of the G0W0 Approximation in Normal and Superconducting States
• Complex Absorbing Potential Green's Function Methods for Resonances
• Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment
• First-principles design of excitonic insulators: A review
• Ab initio GW calculation for organic compounds (TMTSF)2PF6
• Time-dependent exchange-correlation hole and potential of the electron gas
• Ensemble Green's function theory for interacting electrons with degenerate ground states
• Natural orbitals and two-particle correlators as tools for analysis of effective exchange couplings in solids
• Stochastic Real-Time Second-Order Green's Function Theory for Neutral Excitations in Molecules and Nanostructures
• Linear Response Functions Respecting Ward-Takahashi Identity and Fluctuation-Dissipation Theorem within $GW$ Approximation
• Transferability of self-energy correction in tight-binding basis constructed from first principles
• Nonmonotonic band gap evolution in bent phosphorene nanosheets
• Fundamental gaps of quantum dots on the cheap
• Fast computation of the Kohn-Sham susceptibility of large systems
• Self-consistent spin-fluctuation spectrum and correlated electronic structure of actinides
• Self-consistent Spectral Function for Non-Degenerate Coulomb Systems and Analytic Scaling Behaviour
• Electron-magnon dynamics triggered by an ultrashort laser pulse: A real-time Dual $GW$ study
• MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language
• General form of the full electromagnetic Green function in materials physics
• First principles calculations of band offsets at heterovalent $\epsilon$-Ge/In${}_x$Al${}_{1-x}$As interfaces
• Phonon Assisted Exciton Processes in Two-Dimensional Tungsten Monocarbide
• Covariant Bethe-Salpeter approximation in strongly correlated electron systems model
• A real-time approach to frequency-mixing spectroscopies: application to sum and difference frequency generation in two-dimensional crystals
• Many-body \textit{ab initio} study of quasiparticles, optical excitations, and excitonic properties in LiZnAs and ScAgC for photovoltaic applications
• An investigation of the sensitivity of the Fermi surface to the treatment of exchange and correlation
• Position Representation of Effective Electron-Electron Interactions in Solids
• Optical properties and one-particle spectral function in non-ideal plasmas
• Heating and cooling in self-consistent many-body simulations
• Renormalized density matrix downfolding: A rigorous framework in learning emergent models from ab initio many-body calculations
• Analysis of diagonal G and subspace W approximations within fully self-consistent GW calculations for bulk semiconducting systems
• Machine learning for accelerated bandgap prediction in strain-engineered quaternary III-V semiconductors
• Physical and unphysical regimes of self-consistent many-body perturbation theory
• Many body theory beyond GW : towards a complete description of 2-body correlated propagation
• Calculated Spin Fluctuational Pairing Interaction in HgBa2CuO4 using LDA+FLEX Method
• Parquet theory for molecular systems: Formalism and static kernel parquet approximation
• Dressed vertices
• Static treatment of dynamic interactions in the single-orbital Anderson impurity model
• On aspects of self-consistency in the Dyson-Schwinger approach to QED and λ(ϕ^\star ϕ)^2 theories
• Self-consistent random phase approximation and optimized hybrid functionals for solids
• A DFT+$U$+$V$ study of pristine and oxygen-deficient HfO${}_2$ with self-consistent Hubbard parameters
• An all-electron product-basis set: application to plasmon anisotropy in simple metals
• Mean-field approximation of the Hubbard model expressed in a many-body basis
• Nonlinear, band-structure, and surface effects in the interaction of charged particles with solids
• Orbital isotropy of magnetic fluctuations in correlated electron materials induced by Hund's exchange coupling
• Hubbard Physics in the PAW GW Approximation
• Many-body Green's function approach to attosecond nonlinear X-ray spectroscopy
• Shift current in 2D Janus Transition-Metal Dichalcogenides: the role of excitons
• Oxygen doping and polaron magnetic coupling in Alq${}_3$ films
• Many-body calculations of plasmon and phonon satellites in angle-resolved photoelectron spectra using the cumulant expansion approach
• Model-Driven Engineering for Quantum Programming: A Case Study on Ground State Energy Calculation
• Multichannel active-space embedding of atomic multiplets in plane-wave DFT/PAW for core-level spectroscopies
• Reliable Density Functional Theory Predictions of Bandgaps for Materials
• Calculations of Spin Fluctuation Spectral Functions ${\alpha }^{2}F$ in High-Temperature Superconducting Cuprates
• Exciton Superfluidity in 2D Heterostructures from First Principles: The importance of material specific screening
• Density-functional approach to the band gaps of finite and periodic two-dimensional systems
• Stability of vacancy-free crystalline phases of titanium monoxide at high pressure and temperature
• Exact exchange-correlation potential of effectively interacting Kohn-Sham systems
• Theory of interaction-induced charge order in CrSBr
• Gor'kov-Hedin-Baym Equations for Quantum Many-Body Systems with Spin-Dependent Interactions
• Many-body perturbation theory with hybrid density functional theory starting points accelerated by adaptively compressed exchange
• Low-scaling \textit{GW} calculations of quasi-particle energies for extended systems within the numerical atomic orbital framework
• Stochastic sampling of quadrature grids for the evaluation of vibrational expectation values
• Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications
• Exploring epitaxial structures for electrically pumped perovskite lasers: a study of CsPb(Br,I)${}_3$ based on the \textit{ab initio} Bethe-Salpeter equation
• GW space-time method: Energy band-gap of solid hydrogen
• Polarizable Continuum Models and Green's Function $\mathbf{GW}$ Formalism: On the Dynamics of the Solvent Electrons
• Dual-space cluster-diagrammatic approach to nonlocal electronic correlations
• Symmetry adaptation for self-consistent many-body calculations
• Thermal quasi-particle theory
• Uniform electron benchmark for the first-principles $G{W}_0$-Eliashberg theory
• Faddeev Random Phase Approximation applied to molecules
• Cutting rules and positivity in finite temperature many-body theory
• Machine learning approach for vibronically renormalized electronic band structures
• Spin liquid phase in the Hubbard model: Luttinger-Ward analysis of the slave-rotor formalism
• Approaching the Basis Set Limit in Gaussian-Orbital-Based Periodic Calculations with Transferability: Performance of Pure Density Functionals for Simple Semiconductors
• Scalable and predictive spectra of correlated molecules with moment truncated iterated perturbation theory
• Interplay of electronic correlations and chemical bonding in FeN${}_2$ under pressure
• On non-canonical degrees of freedom
• Strong 1D localization and highly anisotropic electron-hole masses in heavy-halogen functionalized graphenes
• Neural network distillation of orbital dependent density functional theory
• Predicting the suitability of photocatalysts for water splitting using Koopmans spectral functionals: The case of TiO${}_2$ polymorphs
• Excited-state band structure mapping
• Many-body description of two-dimensional van der Waals ferroelectric $\alpha -$In${}_2$Se${}_3$
• General Many-Body Perturbation Framework for Moiré Systems