| GW approximation | |
|---|---|
| Name | GW approximation |
| Caption | Schematic of quasiparticle energy correction in the GW method |
| Introduced | 1965 |
| Developers | Lars Hedin |
| Field | Quantum many-body theory |
| Related | Density functional theory, Bethe–Salpeter equation |
GW approximation
The GW approximation is a Green's-function–based perturbative method used to compute quasiparticle energies and electronic excitation properties in interacting electron systems. It approximates the electronic self-energy by the product of the one-particle Green's function (G) and the screened Coulomb interaction (W), and is widely applied to predict band structures, ionization potentials, and electron affinities beyond mean-field theories. GW is essential in condensed matter physics and computational quantum chemistry for improving accuracy over Density functional theory predictions of excited-state observables.
The GW approximation occupies a central role within quantum many-body theory as a first-order expansion of the electronic self-energy in terms of screened interactions. It builds on the one-particle Green's function formalism and the Dyson equation to relate interacting and noninteracting propagators. GW connects to experimental probes such as angle-resolved photoemission spectroscopy (ARPES) and photoelectron spectroscopy by providing theoretical quasiparticle energies. Major conceptual neighbors include the Random-phase approximation (RPA) used to compute screening, the Hedin equations which formally define the self-energy, and diagrammatic perturbation theory developed in the context of Feynman diagram techniques.
Formally, the GW self-energy Σ is given by Σ(1,2) = i G(1,2) W(1,2), where numbers denote space, spin and time coordinates. The screened Coulomb interaction W is computed from the bare Coulomb potential v and the reducible polarizability χ via W = v + v χ W, often evaluated within the Random-phase approximation so that χ ≈ −i G G. The GW approximation is derived as the first term in an expansion of Hedin's coupled set of equations introduced by Lars Hedin in 1965. Practical variants include the non-self-consistent G0W0, partially self-consistent GW0 and eigenvalue-self-consistent evGW, and fully self-consistent GW, each corresponding to different treatments of G and W within the Dyson and polarizability loops.
GW implementations are available in many electronic-structure codes such as Quantum ESPRESSO, VASP, ABINIT, Yambo, BerkeleyGW, FHI-aims, and Gaussian derivatives. Numerical considerations include basis sets (plane waves, Gaussian orbital, or numeric atom-centered orbitals), frequency integration schemes (analytic continuation, contour deformation, or plasmon-pole models), and k-point sampling for periodic systems. Efficient evaluation uses techniques like the plasmon-pole model to approximate frequency-dependent screening, the Sternheimer equation for response functions, and resolution-of-identity / density-fitting to reduce four-index Coulomb integrals. High-performance implementations exploit parallel computing, GPU acceleration, and algorithms for avoiding explicit empty-state summations (e.g., Lanczos and Sternheimer approaches).
GW has been extensively applied to predict quasiparticle band structures of semiconductors and insulators such as silicon, gallium arsenide, and diamond, correcting the band-gap underestimation of typical local density approximation and generalized gradient approximation calculations. In molecular quantum chemistry GW is used to compute ionization potentials and electron affinities of peptides, organic molecules, and clusters. For low-dimensional systems and nanostructures, GW captures reduced screening effects in graphene, transition metal dichalcogenide monolayers (e.g., MoS2), quantum dots, and organic/inorganic interfaces. Combined with the Bethe–Salpeter equation, GW provides optical spectra and exciton binding energies relevant to photovoltaics and optoelectronics.
GW is complementary to Density functional theory: DFT provides ground-state densities and Kohn–Sham eigenvalues often used as starting points for G0W0 calculations. Compared to Hartree–Fock theory, GW includes dynamic screening and avoids the unscreened exchange overestimation of band gaps. The GW quasiparticle energies serve as input to the Bethe–Salpeter equation (BSE) for computing two-particle (electron–hole) excitations and optical absorption spectra. GW can be viewed within many-body perturbation theory as an approximation that improves on static mean-field methods while remaining less costly than full configuration interaction or complete coupled-cluster treatments in large systems.
GW typically yields band gaps and ionization energies in much better agreement with experiment than local or semilocal DFT, but accuracy depends on the starting point and level of self-consistency. Common limitations include sensitivity to the chosen exchange–correlation starting functional, convergence with respect to basis size and unoccupied states, and the neglect of vertex corrections beyond GW which can be important for satellites and strong-correlation physics. Approximations to ameliorate cost or accuracy include G0W0, evGW, GW0, plasmon-pole models, and inclusion of partial vertex corrections (e.g., GWΓ). For strongly correlated materials (e.g., Mott insulators) GW may fail without embedding methods such as Dynamical mean-field theory (DMFT).
The GW approximation was derived by Lars Hedin (1965) within a formal set of equations for the electronic self-energy. Subsequent development and practical adoption involved contributions from researchers such as Walter Kohn (through influence of DFT), Luigi Hedin collaborators, and computational pioneers implementing GW in codes like those from University of California, Berkeley (BerkeleyGW), EPFL and Max Planck Institute for Solid State Research. Key methodological advances include the plasmon-pole model by Hybertsen and Louie (Mark S. Hybertsen and Steven G. Louie), algorithms for avoiding empty-state summations, and integration with BSE by groups studying optical properties. GW continues to evolve through contributions at conferences such as the APS March Meeting and in journals including Physical Review Letters and Physical Review B.
Category:Quantum many-body theory Category:Electronic structure methods