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GW

This page gives hints on how to perform a GW calculation, including self-consistency with the ABINIT package.

Introduction

DFT performs reasonably well for the determination of structural properties, but fails to predict accurate band gaps. A more rigorous framework for the description of excited states is provided by many-body perturbation theory (MBPT) [Fetter1971], [Abrikosov1975], based on the Green’s functions formalism and the concept of quasi-particles [Onida2002].

Within MBPT, one can calculate the quasi-particle (QP) energies, E, and amplitudes, Ψ, by solving a nonlinear equation involving the non-Hermitian, nonlocal and frequency dependent self-energy operator Σ.

This equation goes beyond the mean-field approximation of independent KS particles as it accounts for the dynamic many-body effects in the electron- electron interaction.

Details about the GW implementation in ABINIT can be found here

A typical GW calculation consists of two different steps (following a DFT calculation): first the screened interaction ε-1 is calculated and stored on disk (optdriver=3), then the KS band structure and W are used to evaluate the matrix elements of Σ, finally obtaining the QP corrections (optdriver=4).

The computation of the screened interaction is described in topic_Susceptibility, while the computation of the self-energy is described in topic_SelfEnergy. The frequency meshes, used e.g. for integration along the real and imaginary axes are described in topic_FrequencyMeshMBPT.

GW calculations can be made less memory and CPU time consuming, at the expense of numerical precision, by compiling ABINIT with the option enable_gw_dpc=“no” in the *.ac9 file.

The GW 1-body reduced density matrix (1RDM) from the linearized Dyson equation can be computed, and when used self-consistently with the Galitskii-Migdal correlation, provides an approximation the self-consistent GW total energy.

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Selected Input Files

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Tutorials

  • gw1 tutorial The first tutorial on GW (GW1) deals with the computation of the quasi-particle band gap of Silicon (semiconductor), in the GW approximation (much better than the Kohn-Sham LDA band structure), with a plasmon-pole model.
  • gw2 tutorial The second tutorial on GW (GW2) deals with the computation of the quasi-particle band structure of Aluminum, in the GW approximation (so, much better than the Kohn-Sham LDA band structure) without using the plasmon-pole model.
  • Parallelism of Many-Body Perturbation calculations (GW) allows to speed up the calculation of accurate electronic structures (quasi-particle band structure, including many-body effects).