mirror of https://github.com/abinit/abinit.git
61 lines
2.9 KiB
Markdown
61 lines
2.9 KiB
Markdown
---
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description: How to perform a GW calculation, including self-consistency
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authors: MG
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---
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<!--- This is the source file for this topics. Can be edited. -->
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This page gives hints on how to perform a GW calculation, including self-consistency with the ABINIT package.
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## Introduction
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DFT performs reasonably well for the determination of structural properties,
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but fails to predict accurate band gaps. A more rigorous framework for the
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description of excited states is provided by many-body perturbation theory
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(MBPT) [[cite:Fetter1971]], [[cite:Abrikosov1975]], based on the Green's
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functions formalism and the concept of quasi-particles [[cite:Onida2002]].
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Within MBPT, one can calculate the quasi-particle (QP) energies, E, and
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amplitudes, Ψ, by solving a nonlinear equation involving the non-Hermitian,
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nonlocal and frequency dependent self-energy operator Σ.
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This equation goes beyond the mean-field approximation of independent KS
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particles as it accounts for the dynamic many-body effects in the electron-
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electron interaction.
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Details about the GW implementation in ABINIT can be found [[theory:mbt|here]]
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A typical GW calculation consists of two different steps (following a DFT
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calculation): first the screened interaction ε-1 is calculated and stored on
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disk ([[optdriver]]=3), then the KS band structure and W are used to evaluate
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the matrix elements of Σ, finally obtaining the QP corrections
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([[optdriver]]=4).
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The computation of the screened interaction is described in
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[[topic:Susceptibility]], while the computation of the self-energy is
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described in [[topic:SelfEnergy]]. The frequency meshes, used e.g. for
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integration along the real and imaginary axes are described in
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[[topic:FrequencyMeshMBPT]].
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GW calculations can be made less memory and CPU time consuming,
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at the expense of numerical precision,
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by compiling ABINIT with the option enable_gw_dpc=“no" in the *.ac9 file.
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The GW 1-body reduced density matrix (1RDM) from the linearized Dyson equation
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can be computed, and when used self-consistently with the Galitskii-Migdal correlation, provides an approximation
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the self-consistent GW total energy.
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## Related Input Variables
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{{ related_variables }}
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## Selected Input Files
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{{ selected_input_files }}
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## Tutorials
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* [[tutorial:gw1]] 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.
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* [[tutorial:gw2]] 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.
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* [[tutorial:paral_mbt|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).
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