Category:Low-scaling GW and RPA: Difference between revisions

Latest revision as of 09:05, 21 February 2024

This category shows all tags and articles concerning low scaling GW and RPA algorithms available as of VASP.6 and newer.

Theoretical Background

The Random Phase Approximation (RPA) is a diagrammatic method to determine the groundstate energy of interacting electrons. The computational cost of diagrammatic methods typically exceeds the one of hybrid DFT calculations, since a frequency dependent Hamiltonian is diagonalized. Conventional GW and RPA/ACFDT algorithms typically scale with the forth power of the system size and are, thus, limited to relatively small system sizes. However, by performing all calculations on the imaginary time and imaginary frequency axis one can exploit coarse Fourier transformation compatible grids and obtain a cubic scaling GW and RPA/ACFDT algorithm. These algorithms can be used to study relatively large systems with diagrammatic methods.

Please take a look on the RPA and GW pages for more information about their theoretical formulation.

How to

The following pages contain some general recipes for

RPA: RPA-ACFDT calculations
GW: A practical guide to low-scaling GW calculations can be found here.

Pages in category "Low-scaling GW and RPA"

The following 20 pages are in this category, out of 20 total.

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-All tags and articles concerning low scaling GW and RPA algorithms available as of VASP.6 and newer.
+This category shows all tags and articles concerning low scaling GW and RPA algorithms available as of VASP.6 and newer.
 == Theoretical Background ==
-GW and RPA are post-DFT methods used to solve the many-body problem approximatively.
+The Random Phase Approximation (RPA) is a diagrammatic method to determine the groundstate energy of interacting electrons.
+The computational cost of diagrammatic methods typically exceeds the one of hybrid DFT calculations, since a frequency dependent Hamiltonian is diagonalized. Conventional GW and RPA/ACFDT algorithms typically scale with the forth power of the system size and are, thus, limited to relatively small system sizes.
+However, by performing all calculations on the imaginary time and imaginary frequency axis one can exploit coarse Fourier transformation compatible grids and obtain a cubic scaling GW and RPA/ACFDT algorithm. These algorithms can be used to study relatively large systems with diagrammatic methods.
-RPA stands for the random phase approximation is often used as synonym for the adiabatic connection fluctuation dissipation theorem (ACFDT). RPA/ACFDT provides access to the correlation energy of a system and can be understood in terms of Feynman diagrams as an infinite sum of all bubble diagrams, where excitonic effects (interactions between electrons and holes) are neglected. The RPA/ACFDT is used as a post-processing tool to determine a more accurate groundstate energy.
+Please take a look on the [[RPA/ACFDT: Correlation energy in the Random Phase Approximation|RPA]] and [[The GW approximation of Hedin's equations|GW]] pages for more information about their theoretical formulation.
-The GW approximation goes hand in hand with the RPA, since the very same diagrammatic contributions are taken into account in the screened Coulomb interaction of a system often denoted as W. However, in contrast to the RPA/ACFDT, the GW method provides access to the spectral properties of the system by means of determining the energies of the quasi-particles of a system using a screened exchange-like contribution to the self-energy. The GW approximation is currently one of the most accurate many-body methods to calculate band-gaps.
-The computational cost of diagrammatic methods typically exceeds the one of hybrid DFT calculations, since frequency dependent potentials are considered in the Hamiltonian. Conventional GW and RPA/ACFDT algorithms typically scale with the forth power of the system size and are, thus, limited to relatively small system.
-However, by performing all calculations on the imaginary time and imaginary frequency axis one can exploit coarse FFT grids and obtain a cubic scaling GW and RPA/ACFDT algorithm. These algorithms can be used to study relatively large systems with diagrammatic methods.
 == How to ==
-A practical guide to low-scaling GW calculations can be found [[Practical guide to GW calculations#lowGW|here]]
+The following pages contain some general recipes for
+*RPA: [[ACFDT/RPA calculations#ACFDTR/RPAR| RPA-ACFDT calculations]]
+*GW: A practical guide to low-scaling GW calculations can be found [[Practical guide to GW calculations#lowGW|here]].
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-[[Category:VASP|ACFDT]][[Category:Many-Body Perturbation Theory|Many-Body Perturbation Theory]][[Category:VASP6]]
+[[Category:VASP|ACFDT]][[Category:Many-body perturbation theory]]