Category:Low-scaling GW and RPA - Revision history

Huebsch at 09:05, 21 February 2024

2024-02-21T09:05:47Z

← Older revision		Revision as of 09:05, 21 February 2024
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	[[Category:VASP\|ACFDT]][[Category:Many-body perturbation theory~~]][[Category:VASP6~~]]		[[Category:VASP\|ACFDT]][[Category:Many-body perturbation theory]]

Huebsch at 10:31, 19 July 2022

2022-07-19T10:31:25Z

← Older revision		Revision as of 10:31, 19 July 2022
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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]][[Category:VASP6]]

Kaltakm: /* How to */

2019-07-29T16:19:42Z

How to

← Older revision		Revision as of 16:19, 29 July 2019
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	== How to ==		== 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\|Many-Body Perturbation Theory]][[Category:VASP6]]

Kaltakm: /* Theoretical Background */

2019-07-29T16:16:41Z

Theoretical Background

← Older revision		Revision as of 16:16, 29 July 2019
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	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.		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.

	~~More information~~ on the ~~theory behind RPA is found~~ [[RPA/ACFDT: Correlation energy in the Random Phase Approximation\|~~here~~]].		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.

	== How to ==		== How to ==

Kaltakm: /* Theoretical Background */

2019-07-29T16:13:41Z

Theoretical Background

← Older revision		Revision as of 16:13, 29 July 2019
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	== Theoretical Background ==		== 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.		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.		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.

			More information on the theory behind RPA is found [[RPA/ACFDT: Correlation energy in the Random Phase Approximation\|here]].

	== How to ==		== How to ==

Kaltakm at 15:32, 25 July 2019

2019-07-25T15:32:34Z

← Older revision		Revision as of 15:32, 25 July 2019
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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 ==		== Theoretical Background ==

Kaltakm: /* How to */

2019-07-25T15:30:46Z

How to

← Older revision		Revision as of 15:30, 25 July 2019
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	== How to ==		== How to ==
	A practical guide to low-scaling GW calculations can be found [[Practical guide to GW calculations#lowGW\|here]].		*A practical guide to low-scaling GW calculations can be found [[Practical guide to GW calculations#lowGW\|here]].
	----		----

	[[Category:VASP\|ACFDT]][[Category:Many-Body Perturbation Theory\|Many-Body Perturbation Theory]][[Category:VASP6]]		[[Category:VASP\|ACFDT]][[Category:Many-Body Perturbation Theory\|Many-Body Perturbation Theory]][[Category:VASP6]]

Kaltakm: /* Theoretical Background */

2019-07-25T14:48:52Z

Theoretical Background

← Older revision		Revision as of 14:48, 25 July 2019
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	== Theoretical Background ==		== Theoretical Background ==
	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.		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 ~~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.		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.

	== How to ==		== How to ==

Kaltakm: /* Theoretical Background */

2019-07-25T14:48:05Z

Theoretical Background

← Older revision		Revision as of 14:48, 25 July 2019
Line 2:		Line 2:

	== Theoretical Background ==		== Theoretical Background ==
	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.		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 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.		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.

Kaltakm: /* Theoretical Background */

2019-07-25T14:46:42Z

Theoretical Background

← Older revision		Revision as of 14:46, 25 July 2019
Line 2:		Line 2:

	== Theoretical Background ==		== Theoretical Background ==
	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.		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.
	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.		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.