Category:Bethe-Salpeter equations - Revision history

Csheldon: /* Tutorials */

2025-05-28T13:29:53Z

Tutorials

← Older revision		Revision as of 13:29, 28 May 2025
Line 127:		Line 127:
	== Tutorials ==		== Tutorials ==
	*Tutorial for calculating the frequency-dependent dielectric function with excitonic effects based on the [https://vasp.at/tutorials/latest/bse/ Bethe-Salpeter equation].		*Tutorial for calculating the frequency-dependent dielectric function with excitonic effects based on the [https://vasp.at/tutorials/latest/bse/ Bethe-Salpeter equation].
			<!--
			*Tutorial for calculating x-ray adsorption spectroscopy ([https://vasp.at/tutorials/latest/xas/part2 XAS calculations]) using the BSE.
			-->

	== References ==		== References ==

	[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]		[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]

Csheldon: /* How to */

2025-05-28T13:28:49Z

How to

← Older revision		Revision as of 13:28, 28 May 2025
Line 124:		Line 124:
	* Practical guide for using the [[Bethe-Salpeter equation for core excitations]]		* Practical guide for using the [[Bethe-Salpeter equation for core excitations]]
	* Practical guide for optimizing the [[Best practices for Bethe-Salpeter calculations\|BSE calculations]]		* Practical guide for optimizing the [[Best practices for Bethe-Salpeter calculations\|BSE calculations]]

			== Tutorials ==
			*Tutorial for calculating the frequency-dependent dielectric function with excitonic effects based on the [https://vasp.at/tutorials/latest/bse/ Bethe-Salpeter equation].

	== References ==		== References ==

	[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]		[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]

Tal: /* How to */

2025-02-21T16:23:04Z

How to

← Older revision		Revision as of 16:23, 21 February 2025
Line 123:		Line 123:
	* Practical guide for solving the Casida equation via diagonalization [[TDDFT calculations]]		* Practical guide for solving the Casida equation via diagonalization [[TDDFT calculations]]
	* Practical guide for using the [[Bethe-Salpeter equation for core excitations]]		* Practical guide for using the [[Bethe-Salpeter equation for core excitations]]
			* Practical guide for optimizing the [[Best practices for Bethe-Salpeter calculations\|BSE calculations]]

	== References ==		== References ==

	[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]		[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]

Tal at 14:29, 21 February 2025

2025-02-21T14:29:53Z

← Older revision		Revision as of 14:29, 21 February 2025
Line 101:		Line 101:
	</math>		</math>
	-->		-->
			== X-ray absorption spectra ==
			The BSE/TDHF algorithm can also be used to model the X-ray absorption spectra (XAS), i.e., excitations from the core states into conduction bands. The detailed documentation of this method can be found in [[:Category:XAS]].
	== Performing BSE calculations on GPU ==		== Performing BSE calculations on GPU ==
	As of VASP 6.5, the BSE/TDHF calculations with {{TAGO\|IBSE\|1}} or {{TAGO\|IBSE\|2}} can be fully run on NVIDIA GPUs.		As of VASP 6.5, the BSE/TDHF calculations with {{TAGO\|IBSE\|1}} or {{TAGO\|IBSE\|2}} can be fully run on NVIDIA GPUs.
Line 120:		Line 122:
	* Practical guide for solving the Bethe-Salpeter equation via diagonalization [[BSE calculations]]		* Practical guide for solving the Bethe-Salpeter equation via diagonalization [[BSE calculations]]
	* Practical guide for solving the Casida equation via diagonalization [[TDDFT calculations]]		* Practical guide for solving the Casida equation via diagonalization [[TDDFT calculations]]
			* Practical guide for using the [[Bethe-Salpeter equation for core excitations]]

	== References ==		== References ==

	[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]		[[Category:VASP\|Bethe-Salpeter equation]][[Category:Many-body perturbation theory]]

Tal: /* Theory */

2025-02-21T11:50:15Z

Theory

← Older revision		Revision as of 11:50, 21 February 2025
Line 18:		Line 18:
	\end{array}\right)~.		\end{array}\right)~.
	</math>		</math>
	Using the eigenvectors and eigenvalues of this equation we can find the dielectric function including the excitonic effects.		Using the eigenvectors <math>\mathbf{X}_\lambda, \mathbf{Y}_\lambda</math> and eigenvalues <math>\omega_\lambda</math> of this equation we can find the dielectric function including the excitonic effects.

	== Scaling ==		== Scaling ==

Tal: /* Theory */

2025-02-21T11:49:00Z

Theory

← Older revision		Revision as of 11:49, 21 February 2025
Line 18:		Line 18:
	\end{array}\right)~.		\end{array}\right)~.
	</math>		</math>
	~~The~~ eigenvalues of this equation ~~correspond to~~ the ~~excitation energies~~ including the excitonic effects~~, i.e., the electron-hole interaction~~.		Using the eigenvectors and eigenvalues of this equation we can find the dielectric function including the excitonic effects.

	== Scaling ==		== Scaling ==

Tal: /* Theory */

2025-02-21T11:45:48Z

Theory

← Older revision		Revision as of 11:45, 21 February 2025
Line 2:		Line 2:

	== Theory ==		== Theory ==
	As discussed in detail in the [[Bethe-Salpeter equation\|theory page]], the Bethe-Salpeter equation is a ~~Dyson like equation for the polarizability <math>L</math>~~		As discussed in detail in the [[Bethe-Salpeter equation\|theory page]], the Bethe-Salpeter equation is a non-hermitian eigenvalue problem
	::<math>		::<math>
	L(\~~omega~~)~~=L_0~~(\~~omega~~)~~+L_0~~(\~~omega~~)~~[v-W]L~~(\~~omega~~),		\left(\begin{array}{cc}
			\mathbf{A} & \mathbf{B} \\
			\mathbf{B}^* & \mathbf{A}^*
			\end{array}\right)\left(\begin{array}{l}
			\mathbf{X}_\lambda \\
			\mathbf{Y}_\lambda
			\end{array}\right)=\omega_\lambda\left(\begin{array}{cc}
			\mathbf{1} & \mathbf{0} \\
			\mathbf{0} & -\mathbf{1}
			\end{array}\right)\left(\begin{array}{l}
			\mathbf{X}_\lambda \\
			\mathbf{Y}_\lambda
			\end{array}\right)~.
	</math>		</math>
	~~where~~ the ~~effective interaction between particles is described by two terms:~~ the ~~bare Coulomb interaction <math>v</math> and the screened interaction <math>W</math>~~.		The eigenvalues of this equation correspond to the excitation energies including the excitonic effects, i.e., the electron-hole interaction.
	~~In practice~~, the ~~solution of this equation is found in transition space, where it can be formulated as an eigenvalue problem~~.

	== Scaling ==		== Scaling ==

Tal at 17:17, 20 February 2025

2025-02-20T17:17:08Z

← Older revision		Revision as of 17:17, 20 February 2025
Line 6:		Line 6:
	L(\omega)=L_0(\omega)+L_0(\omega)[v-W]L(\omega),		L(\omega)=L_0(\omega)+L_0(\omega)[v-W]L(\omega),
	</math>		</math>
	where the effective interaction between particles is described by two terms, the bare Coulomb <math>v</math> and the screened interaction <math>W</math>.		where the effective interaction between particles is described by two terms: the bare Coulomb interaction <math>v</math> and the screened interaction <math>W</math>.
	In practice, the solution of this equation is found in transition space, where it can be formulated as an eigenvalue problem.		In practice, the solution of this equation is found in transition space, where it can be formulated as an eigenvalue problem.

Tal: /* Theory */

2025-02-20T16:53:57Z

Theory

← Older revision		Revision as of 16:53, 20 February 2025
Line 2:		Line 2:

	== Theory ==		== Theory ==
	As discussed in detail in the [[Bethe-Salpeter equation\|theory page]], the Bethe-Salpeter equation is a Dyson like equation for the ~~two-particle~~ polarizability <math>L</math>		As discussed in detail in the [[Bethe-Salpeter equation\|theory page]], the Bethe-Salpeter equation is a Dyson like equation for the polarizability <math>L</math>
	::<math>		::<math>
	L(\omega)=L_0(\omega)+L_0(\omega)[v-W]L(\omega),		L(\omega)=L_0(\omega)+L_0(\omega)[v-W]L(\omega),

Tal: /* Theory */

2025-02-20T16:37:09Z

Theory

@@ Line 2: / Line 2: @@
 == Theory ==
-=== Bethe-Salpeter equation ===
+As discussed in detail in the [[Bethe-Salpeter equation|theory page]], the Bethe-Salpeter equation is a Dyson like equation for the two-particle polarizability <math>L</math>
 ::<math>
-\left(\begin{array}{cc}
+L(\omega)=L_0(\omega)+L_0(\omega)[v-W]L(\omega),
 </math>
+where the effective interaction between particles is described by two terms, the bare Coulomb <math>v</math> and the screened interaction <math>W</math>.
+In practice, the solution of this equation is found in transition space, where it can be formulated as an eigenvalue problem.
 == Scaling ==