Category:Strongly correlated electrons - Revision history

Csheldon: /* Dynamical mean-field theory (DMFT) */

2026-07-20T08:30:53Z

Dynamical mean-field theory (DMFT)

← Older revision		Revision as of 08:30, 20 July 2026
Line 52:		Line 52:
	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

	* Lecture on ~~the~~ {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}}.		* Lecture on {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}}.
	* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.		* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.
	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

Csheldon: /* Dynamical mean-field theory (DMFT) */

2026-07-20T08:30:34Z

Dynamical mean-field theory (DMFT)

← Older revision		Revision as of 08:30, 20 July 2026
Line 52:		Line 52:
	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

	* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}} ~~(DMFT)~~.		* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}}.
	* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.		* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.
	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

Csheldon: /* Dynamical mean-field theory (DMFT) */

2026-07-20T08:30:24Z

Dynamical mean-field theory (DMFT)

← Older revision		Revision as of 08:30, 20 July 2026
Line 52:		Line 52:
	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

	~~<!--~~		* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}} (DMFT).
	* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}} (DMFT).~~-->~~
	* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.		* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.
	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

Csheldon at 10:10, 2 July 2026

2026-07-02T10:10:37Z

← Older revision		Revision as of 10:10, 2 July 2026
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	:[[Constrained–random-phase–approximation formalism#Effective Coulomb kernel in constrained random-phase approximation\|VASP provides several approaches for calculating <math>\chi_d</math>]]		:[[Constrained–random-phase–approximation formalism#Effective Coulomb kernel in constrained random-phase approximation\|VASP provides several approaches for calculating <math>\chi_d</math>]]

	:* Lecture on the {{Video\|~~str_corr~~:merzuk:2026\|constrained random-phase approximation}} (cRPA).		:* Lecture on the {{Video\|strong_corr:merzuk:2026\|constrained random-phase approximation}} (cRPA).
			:* Tutorial for {{Tutorial\|strong_corr:part1\|cRPA of NiO}}.
	:* Workflow for [[CRPA of SrVO3]].		:* Workflow for [[CRPA of SrVO3]].

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	where the first term is the standard DFT energy, the second term is the Hubbard on-site interaction and the third term accounts for the double counting. The on-site interaction is described by <math>U^I</math> and <math>n_m^{I\sigma}</math> are occupation numbers that are defined as projections of occupied Kohn-Sham orbitals on the states of a localized basis set.		where the first term is the standard DFT energy, the second term is the Hubbard on-site interaction and the third term accounts for the double counting. The on-site interaction is described by <math>U^I</math> and <math>n_m^{I\sigma}</math> are occupation numbers that are defined as projections of occupied Kohn-Sham orbitals on the states of a localized basis set.
			<!--
			* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U}}.-->
			* Tutorial for {{Tutorial\|strong_corr:part2\|DFT+U on NiO}}.
			* Tutorial for {{Tutorial\|strong_corr:part3\|GW and DFT+U on NiO}}.
	* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.		* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.
	* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.		* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.
Line 48:		Line 52:
	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

			<!--
			* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}} (DMFT).-->
			* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.
	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

Huebsch at 09:43, 17 June 2026

2026-06-17T09:43:10Z

← Older revision		Revision as of 09:43, 17 June 2026
Line 46:		Line 46:

	== Dynamical mean-field theory (DMFT) ==		== Dynamical mean-field theory (DMFT) ==
	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. ~~A key~~ quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

Huebsch at 09:38, 17 June 2026

2026-06-17T09:38:35Z

← Older revision		Revision as of 09:38, 17 June 2026
Line 46:		Line 46:

	== Dynamical mean-field theory (DMFT) ==		== Dynamical mean-field theory (DMFT) ==
	[[DFT+DMFT calculations~~\|DMFT~~]] ~~is a dynamical extension of DFT+U that provides a more accurate treatment of strongly correlated materials where DFT+U is insufficient~~ {{cite\|kotliar:rmp:2006}}~~. Like DFT+U, DMFT~~ augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. The central approximation is that the self-energy is ~~purely local —~~ frequency-dependent but momentum-independent. ~~This makes the problem tractable while still capturing~~ many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction ~~parameters~~ entering DMFT can be determined ~~from first principles using cRPA (see~~ [[~~Constrained–random~~-~~phase–approximation formalism~~\|~~cRPA section above~~]]).		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. A key quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

	* Workflow for [~~https://vasp.at/wiki/~~DFT%2BDMFT_calculations NiO DFT+DMFT calculations].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

	== Other methods ==		== Other methods ==

Huebsch at 09:15, 17 June 2026

2026-06-17T09:15:08Z

Show changes

Csheldon: /* Hybrid functionals + U */

2026-06-15T10:58:43Z

Hybrid functionals + U

← Older revision		Revision as of 10:58, 15 June 2026
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	=== Hybrid functionals + U ===		=== Hybrid functionals + U ===
	A well-known limitation of hybrid functionals is their uniform treatment of all electronic states, which can result in markedly different levels of accuracy for states with varying degrees of localization. The inclusion of the Hubbard on-site interaction term within the hybrid functional framework has been shown to address inaccuracies arising from the overscreening of localized states {{cite\|Ivady2014}}.		A well-known limitation of hybrid functionals is their uniform treatment of all electronic states, which can result in markedly different levels of accuracy for states with varying degrees of localization. The inclusion of the Hubbard on-site interaction term within the hybrid functional framework ([[:Category:Exchange-correlation functionals#Density functional theory plus U (DFT+U)\|hybrid + U]]) has been shown to address inaccuracies arising from the overscreening of localized states {{cite\|Ivady2014}}.

	=== Quasi-particle GW (QPGW) ===		=== Quasi-particle GW (QPGW) ===

Csheldon at 10:43, 15 June 2026

2026-06-15T10:43:16Z

← Older revision		Revision as of 10:43, 15 June 2026
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	==== Additional ====-->		==== Additional ====-->
	* Tutorial for {{Tutorial\|transition_states:part1\|NEB, IDM, elbow plot, and IRC calculations}}.
	* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.		* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.
	* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.		* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.

Csheldon: /* Tutorials */

2026-06-15T10:42:36Z

Tutorials

← Older revision		Revision as of 10:42, 15 June 2026
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	* ''Dynamical Mean-Field Theory for Strongly Correlated Materials'' by Volodymyr Turkowski - a book about DMFT {{Cite\|turkowski:book:2021}}.		* ''Dynamical Mean-Field Theory for Strongly Correlated Materials'' by Volodymyr Turkowski - a book about DMFT {{Cite\|turkowski:book:2021}}.

	=== Tutorials ===		=== Tutorials ===<!--
			* Tutorial for {{Tutorial\|strong_corr:part1\|constrained random-phase approximation (cRPA)}}.
			* Tutorial for {{Tutorial\|strong_corr:part2\|DFT+U and dynamical mean-field theory (DMFT)}}.
			* Tutorial for {{Tutorial\|strong_corr:part3\|Bethe-Salpeter equation (BSE)}}.

			==== Additional ====-->
			* Tutorial for {{Tutorial\|transition_states:part1\|NEB, IDM, elbow plot, and IRC calculations}}.
	* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.		* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.
	* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.		* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.

← Older revision		Revision as of 08:30, 20 July 2026
Line 52:		Line 52:
	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

	* Lecture on ~~the~~ {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}}.		* Lecture on {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}}.
	* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.		* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.
	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

← Older revision		Revision as of 08:30, 20 July 2026
Line 52:		Line 52:
	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

	* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}} ~~(DMFT)~~.		* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}}.
	* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.		* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.
	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

← Older revision		Revision as of 08:30, 20 July 2026
Line 52:		Line 52:
	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

	~~<!--~~		* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}} (DMFT).
	* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}} (DMFT).~~-->~~
	* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.		* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.
	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

← Older revision		Revision as of 10:10, 2 July 2026
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	:[[Constrained–random-phase–approximation formalism#Effective Coulomb kernel in constrained random-phase approximation\|VASP provides several approaches for calculating <math>\chi_d</math>]]		:[[Constrained–random-phase–approximation formalism#Effective Coulomb kernel in constrained random-phase approximation\|VASP provides several approaches for calculating <math>\chi_d</math>]]

	:* Lecture on the {{Video\|~~str_corr~~:merzuk:2026\|constrained random-phase approximation}} (cRPA).		:* Lecture on the {{Video\|strong_corr:merzuk:2026\|constrained random-phase approximation}} (cRPA).
			:* Tutorial for {{Tutorial\|strong_corr:part1\|cRPA of NiO}}.
	:* Workflow for [[CRPA of SrVO3]].		:* Workflow for [[CRPA of SrVO3]].

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	where the first term is the standard DFT energy, the second term is the Hubbard on-site interaction and the third term accounts for the double counting. The on-site interaction is described by <math>U^I</math> and <math>n_m^{I\sigma}</math> are occupation numbers that are defined as projections of occupied Kohn-Sham orbitals on the states of a localized basis set.		where the first term is the standard DFT energy, the second term is the Hubbard on-site interaction and the third term accounts for the double counting. The on-site interaction is described by <math>U^I</math> and <math>n_m^{I\sigma}</math> are occupation numbers that are defined as projections of occupied Kohn-Sham orbitals on the states of a localized basis set.
			<!--
			* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U}}.-->
			* Tutorial for {{Tutorial\|strong_corr:part2\|DFT+U on NiO}}.
			* Tutorial for {{Tutorial\|strong_corr:part3\|GW and DFT+U on NiO}}.
	* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.		* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.
	* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.		* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.
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	In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].		In [[DFT+DMFT calculations]], DMFT{{cite\|kotliar:rmp:2006}} augments the DFT calculation with an additional local correlated subproblem — typically a specific <math>d</math>- or <math>f</math>-shell. The key idea is to map the full lattice problem onto a quantum impurity model: a single correlated site embedded in a self-consistently determined effective bath representing the rest of the lattice. DMFT can be discussed using the [[GW_approximation_of_Hedin%27s_equations#Green's_functions\|Green's function formalism]] also used in the context of [[many-body perturbation theory]]. The main quantity is the electronic self-energy. Within DMFT it is defined as the sum of all one-particle irreducible diagrams. The central approximation is that the self-energy is frequency-dependent but momentum-independent, i.e., purely local. [[DFT+DMFT calculations]] capture many-body effects beyond the reach of DFT+U, such as quasiparticle mass renormalization, Hubbard bands, and the Mott metal–insulator transition. The interaction parameter entering DMFT can be determined as discussed in [[#Estimating the on-site Coulomb interaction U\|estimating the on-site Coulomb interaction U]].

			<!--
			* Lecture on the {{Video\|strong_corr:alex:2026\|DFT+U and dynamical mean-field theory}} (DMFT).-->
			* Tutorial for {{Tutorial\|strong_corr:part2\|DMFT on NiO}}.
	* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].		* Workflow for [[DFT%2BDMFT_calculations\|NiO DFT+DMFT calculations]].

← Older revision		Revision as of 10:42, 15 June 2026
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	* ''Dynamical Mean-Field Theory for Strongly Correlated Materials'' by Volodymyr Turkowski - a book about DMFT {{Cite\|turkowski:book:2021}}.		* ''Dynamical Mean-Field Theory for Strongly Correlated Materials'' by Volodymyr Turkowski - a book about DMFT {{Cite\|turkowski:book:2021}}.

	=== Tutorials ===		=== Tutorials ===<!--
			* Tutorial for {{Tutorial\|strong_corr:part1\|constrained random-phase approximation (cRPA)}}.
			* Tutorial for {{Tutorial\|strong_corr:part2\|DFT+U and dynamical mean-field theory (DMFT)}}.
			* Tutorial for {{Tutorial\|strong_corr:part3\|Bethe-Salpeter equation (BSE)}}.

			==== Additional ====-->
			* Tutorial for {{Tutorial\|transition_states:part1\|NEB, IDM, elbow plot, and IRC calculations}}.
	* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.		* Tutorial for {{Tutorial\|bulk:e09\|NiO DFT+U calculations}}.
	* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.		* Tutorial for {{Tutorial\|magnetism:e03\|antiferromagnetic NiO}}.