| GW approximation | |
|---|---|
| Name | GW approximation |
| Caption | Schematic of quasiparticle self-energy in the GW approximation |
| Field | Condensed matter physics |
| Introduced | 1965 |
| Developers | Lars Hedin |
| Related | Many-body perturbation theory, Density functional theory, Green's functions |
GW approximation
The GW approximation is a perturbative method in many-body perturbation theory used to compute electronic excitations and quasiparticle energies 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, improving on Density functional theory predictions for band structures, band gaps, and spectral properties. GW matters in quantum physics and materials science by providing a bridge between ab initio calculations and experimentally measurable spectroscopies such as photoemission spectroscopy.
The GW approximation was introduced by Lars Hedin in 1965 within the formalism of many-body physics to capture dynamical screening effects absent from mean-field theories. Conceptually, it replaces the exact self-energy Σ by Σ ≈ iGW, where screening described by W accounts for polarization of the electron gas and collective modes like plasmons. It is used to compute quasiparticle energies that correspond to poles of the interacting Green's function and can be compared with measurements from angle-resolved photoemission spectroscopy (ARPES) and inverse photoemission. GW sits alongside methods such as Hartree–Fock, Configuration interaction, and Coupled cluster theories, forming a practical middle ground between accuracy and computational cost.
At the core is Hedin's set of coupled equations: G, the self-energy Σ, the polarization P, the vertex function Γ, and the screened interaction W. In practice the GW approximation sets Γ ≈ 1, yielding Σ(r,r';ω) = i ∫ dω' G(r,r';ω+ω') W(r,r';ω') e^{iηω'}. W is computed from the bare Coulomb interaction v and the polarization P via W = v + vPW, often evaluated in the random phase approximation (RPA). The quasiparticle equation is typically solved perturbatively: E_nk^QP = E_nk^KS + ⟨ψ_nk|Σ(E_nk^QP) − V_xc|ψ_nk⟩, linking GW with Kohn–Sham eigenvalues from Density functional theory and exchange–correlation potential V_xc. Frequency dependence, analytic continuation, and treatment of singularities require care; common numerical strategies include plasmon-pole models and contour-deformation techniques.
GW calculations are implemented in electronic structure packages such as BerkeleyGW, Yambo, VASP, Quantum ESPRESSO, ABINIT, and SPR-KKR. Practical implementations must handle large basis sets (plane waves, Wannier functions, or localized orbitals), Brillouin zone sampling, and convergence of empty states. Algorithms include one-shot G0W0, partially self-consistent GW0 or GW, and quasiparticle self-consistent GW (QS GW). Efficient evaluation uses techniques like the fast Fourier transform (FFT), resolution-of-identity (RI) density fitting, and analytic continuation via Padé approximants. High-performance computing resources—from university clusters to national facilities such as Argonne National Laboratory and Oak Ridge National Laboratory—enable GW studies of realistic materials, while software projects often emphasize open-science, reproducibility, and community benchmarks.
GW has been instrumental in predicting and explaining electronic properties of semiconductors (e.g., silicon, Gallium arsenide), insulators (e.g., diamond), two-dimensional materials like Graphene and Transition metal dichalcogenides (TMDCs), and complex oxides. It corrects band gaps underestimated by common exchange–correlation functionals in DFT, refines defect level positions crucial for photovoltaics and LED materials, and helps interpret spectroscopic signatures from X-ray photoelectron spectroscopy (XPS) and ARPES. GW combined with the Bethe–Salpeter equation (BSE) yields optical excitation spectra and exciton binding energies, informing research in optoelectronics and quantum materials design.
Limitations include high computational cost, sensitivity to starting-point dependence in G0W0, and challenges for strongly correlated systems where local interactions dominate (e.g., Mott insulators). Extensions address these issues: GW+DMFT couples GW with Dynamical mean field theory to treat local correlations; vertex-corrected GW incorporates beyond-Γ=1 effects; and stochastic GW and low-scaling algorithms seek tractable scaling for large systems. Recent developments emphasize reproducibility, community benchmarking (e.g., GW100 benchmark), incorporation of spin–orbit coupling for heavy elements, and equitable access to software and high-performance resources. From a social perspective, advocates within the computational materials community push for open-source tools and diverse participation to ensure benefits of predictive materials modeling are broadly shared across industry, academia, and under-resourced regions.
GW serves as an accessible case study in advanced Quantum mechanics and many-body courses, illustrating diagrammatic expansions, polarization, and collective excitations. It connects formal concepts—such as Dyson's equation, quasiparticles, and spectral functions—with computational practice and experimental observables. Educational materials and workshops by institutions like Max Planck Society, CERN theory schools, and university courses increasingly integrate hands-on GW tutorials using community codes to reduce barriers for students from underrepresented backgrounds. Pedagogically, GW fosters interdisciplinary training combining physics, numerical analysis, and high-performance computing, aligning technical excellence with goals of inclusion and equitable scientific capacity building.
Category:Electronic structure methods Category:Many-body theory