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| GW approximation | |
|---|---|
| Name | GW approximation |
| Caption | Schematic of quasiparticle energy correction in many-body perturbation theory |
| Field | Condensed matter physics, Materials science, Computational chemistry |
| Introduced | 1965 |
| Originated | United Kingdom; United States |
| Notable persons | Lars Hedin, Walter Kohn, Lu Jeu Sham, John Pople, Richard Feynman |
GW approximation The GW approximation is a many-body perturbation theory method for calculating quasiparticle energies and electronic excitations in solids, molecules, and nanostructures. It corrects mean-field electronic structure results by approximating the electron self-energy as the product of the one-particle Green's function and the screened Coulomb interaction. The technique is widely used alongside density functional theory and quantum chemistry methods to predict band structures, ionization potentials, and electron affinities with improved accuracy.
The GW approximation refines starting points such as Kohn–Sham equations from Density functional theory implementations like Local density approximation and Generalized gradient approximation by introducing many-body effects through the self-energy Σ ≈ iGW. It sits within the framework of Many-body perturbation theory and is often contrasted with wavefunction methods developed by John Pople and post-Hartree–Fock approaches used in Quantum chemistry. Implementations appear in software originating from institutions such as Lawrence Berkeley National Laboratory, Argonne National Laboratory, Max Planck Society, MIT, and ETH Zurich.
The formal basis stems from Green's function techniques introduced in quantum field theory by figures such as Richard Feynman and further developed in solid-state contexts by Lars Hedin. Hedin derived a closed set of equations—Green's function G, self-energy Σ, polarizability P, screened interaction W, and vertex function Γ—linking to formulations by Lev Landau on quasiparticles and Lev Davidovich Landau's Fermi liquid theory. The GW approximation neglects vertex corrections by setting Γ → 1, yielding Σ = iGW. This connects to screening concepts from David Bohm, dielectric response models like the Random phase approximation, and many techniques used in Band theory of solids and Electronic band structure calculations practiced at places like Bell Labs and IBM Research.
Practical GW computations begin with a mean-field input from codes inspired by projects at MIT, Princeton University, University of California, Berkeley, California Institute of Technology, and Oak Ridge National Laboratory. Algorithms implement frequency and momentum (k-point) integrations, plasmon-pole models, contour deformation, and analytic continuation strategies used in packages developed by teams affiliated with Swiss Federal Institute of Technology in Zurich, Max Planck Society, Stanford University, Harvard University, and Yale University. Techniques include one-shot G0W0, partially self-consistent GW0 and eigenvalue-self-consistent evGW, and fully self-consistent GW, each influenced by computational frameworks like plane-wave bases from Paul Dirac-inspired pseudopotential formalisms and localized basis sets championed by groups at University of Cambridge and Imperial College London. High-performance implementations exploit architectures by Intel Corporation, NVIDIA, and supercomputing centres such as Oak Ridge Leadership Computing Facility and Argonne Leadership Computing Facility.
GW is applied to predict band gaps in semiconductors studied at Bell Labs, optical properties of transition metal oxides investigated by researchers at Argonne National Laboratory and Brookhaven National Laboratory, and quasiparticle spectra of molecules examined by teams at Columbia University and University of Chicago. It informs materials design efforts at Lawrence Berkeley National Laboratory and device modeling in collaborations with Samsung Electronics and Intel Corporation. GW results feed into Bethe–Salpeter equation calculations for excitons in materials relevant to Sony Corporation and Samsung Electronics' photovoltaic research, and are used alongside time-dependent density functional theory workflows developed at Trinity College, Cambridge and Yale University.
GW improves quantitatively upon Local density approximation and Generalized gradient approximation band gaps but may depend on the starting point from mean-field theories like Hartree–Fock or hybrid functionals pioneered by Walter Kohn and Lu Jeu Sham. Limitations include neglect of vertex corrections important in strongly correlated systems studied at Rutgers University and failures for certain transition metal oxides investigated at University of California, Los Angeles. Extensions incorporate vertex functions (GWΓ), cumulant expansions used by researchers at Columbia University and University of Pennsylvania, and combinations with dynamical mean-field theory (GW+DMFT) developed in collaborations with Max Planck Institute for Solid State Research and École Normale Supérieure. Benchmarks against quantum Monte Carlo data from groups at Princeton University and University of Illinois Urbana–Champaign and comparisons to highly correlated methods by John Pople-style quantum chemistry validate GW performance across materials studied at National Institute of Standards and Technology.
The GW approximation originated in the mid-1960s through work by Lars Hedin following theoretical foundations laid by Richard Feynman, Lev Landau, and contributors to Green's function methods at Bell Labs and Brookhaven National Laboratory. Subsequent computational and methodological advances involved researchers and institutions including Walter Kohn and collaborators at University of California, San Diego, numerical implementations by groups at Max Planck Society, and widespread adoption driven by electronic structure communities at MIT, University of Cambridge, ETH Zurich, and Princeton University. Modern developments in GW theory and software have been advanced by multidisciplinary teams spanning national laboratories such as Lawrence Berkeley National Laboratory, Argonne National Laboratory, and companies like Microsoft Research and IBM Research.