Many-Body Perturbation Theory in Electronic Structure and Correlation

Many-body perturbation theory provides a systematic route to describe electronic interactions beyond mean-field approaches by treating electron–electron correlation as a series of corrections to a noninteracting reference. Central to this framework are Green’s functions, which encode how single particles propagate in the presence of interactions, and the self-energy operator, which captures exchange and correlation effects. The GW approximation yields accurate quasiparticle energies by combining the one-particle Green’s function with a dynamically screened Coulomb interaction, while the Bethe–Salpeter equation extends this to neutral excitations by solving for correlated electron–hole pairs. Such methods have become indispensable for predicting band gaps, optical spectra and charge-transport properties in semiconductors, molecular materials and low-dimensional systems. By reconciling quantum-chemical accuracy with computational tractability, many-body perturbation theory underpins the design of next-generation photovoltaics, light-emitting diodes and quantum information platforms.

Research from Nature Portfolio

A novel algorithm has been introduced that accelerates fully converged GW calculations for large systems by up to two orders of magnitude without compromising numerical accuracy. By optimising the representation of the screened interaction and exploiting sparsity in the self-energy evaluation, the method enables quasiparticle predictions on supercells containing hundreds of atoms, achieving errors below 0.03 eV. Demonstrations on oxide semiconductors such as zinc oxide and magnesium oxide, as well as emerging two-dimensional materials, showcase its capacity to bring precise excited-state modelling within reach for complex heterostructures and nanostructures.

Many-Body Perturbation Theory in Electronic Structure and Correlation publication trend

The graph below shows the total number of articles in many-body perturbation theory in electronic structure and correlation across all publications each year (not limited to Nature Index journals).

Technical terms

Many-body perturbation theory: A framework that describes interactions among multiple electrons by expanding physical quantities around a noninteracting reference.

Green’s function: A mathematical object capturing the propagation of an electron or excitation in a system including interactions.

GW approximation: An approach in which the electronic self-energy is approximated by the product of the Green’s function (G) and the screened Coulomb interaction (W).

Bethe–Salpeter equation: An equation used to compute correlated electron–hole excitations based on the two-particle Green’s function.

Embedding: A strategy in which a region of interest is treated with a high-level theory and surrounded by an environment described at a lower level.

Dynamical screening: The frequency-dependent modification of the Coulomb interaction due to the response of other electrons.

Quasiparticle: A concept representing an electron or hole excitation dressed by interactions with its environment, carrying effective energy and lifetime.

References

1. Embedded Many‐Body Green's Function Methods for Electronic Excitations in Complex Molecular Systems. Wiley Interdisciplinary Reviews Computational Molecular Science (2024).
2. Dynamical downfolding for localized quantum states. npj Computational Materials (2023).
3. Speeding up GW Calculations to Meet the Challenge of Large Scale Quasiparticle Predictions. Scientific Reports (2016).