LSCRPA: Difference between revisions
(Created page with "{{TAGDEF|LSCRPA|[logical]|.FALSE.}} Description: {{TAG|LSCRPA}} selects the spectral cRPA method. ---- Selects the spectral cRPA method where following screening effects are subtracted from the full RPA polarizability ::<math>\tilde \chi^\sigma_{{\bf G,G}'}({\bf q},i\omega)\approx \frac 1{N_k}\sum_{nn'{\bf k}} \frac{ f_{n\bf k}-f_{n'\bf k-q} }{ \epsilon_{n{\bf k}} - \epsilon_{n'\bf k-q} - i \ome...") |
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Description: {{TAG|LSCRPA}} selects the [[Constrained–random-phase–approximation_formalism#Weighted_method|spectral cRPA method]]. | Description: {{TAG|LSCRPA}} selects the [[Constrained–random-phase–approximation_formalism#Weighted_method|spectral cRPA method]]. | ||
---- | ---- | ||
When selected the spectral method in constrained RPA (cRPA) calculations is selected. The screening effects in the target space are calculated as follows | |||
::<math>\tilde \chi^\sigma_{{\bf G,G}'}({\bf q},i\omega)\approx | ::<math>\tilde \chi^\sigma_{{\bf G,G}'}({\bf q},i\omega)\approx | ||
\frac 1{N_k}\sum_{nn'{\bf k}} | \frac 1{N_k}\sum_{nn'{\bf k}} | ||
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Here <math>\theta_{n{\bf k}}^\sigma</math> are the eigenvalues of the [[Constrained–random-phase–approximation_formalism#Projector_method|correlated projectors]] <math> | Here <math>\theta_{n{\bf k}}^\sigma</math> are the eigenvalues of the [[Constrained–random-phase–approximation_formalism#Projector_method|correlated projectors]] <math> | ||
P_{mn}^{\sigma({\bf k})} = \sum_{i\in \cal T} T_{i m}^{*\sigma({\bf k})} T_{i n}^{\sigma({\bf k})} | P_{mn}^{\sigma({\bf k})} = \sum_{i\in \cal T} T_{i m}^{*\sigma({\bf k})} T_{i n}^{\sigma({\bf k})} | ||
</math> ordered according to their leverage scores. This method results in larger effective interactions compared to [[Constrained–random-phase–approximation_formalism#Weighted_method|w-cRPA]] or the [[Constrained–random-phase–approximation_formalism#Projector_method|projector method]]. | </math> ordered according to their leverage scores. This method results in larger effective interactions compared to [[Constrained–random-phase–approximation_formalism#Weighted_method|w-cRPA]] or the [[Constrained–random-phase–approximation_formalism#Projector_method|projector method]] and conserves the number of electrons. | ||
== Related tags and articles== | == Related tags and articles== | ||
{{TAG|LDISENTANGLED}}, | {{TAG|LDISENTANGLED}}, | ||
Revision as of 15:21, 25 March 2025
LSCRPA = [logical]
Default: LSCRPA = .FALSE.
Description: LSCRPA selects the spectral cRPA method.
When selected the spectral method in constrained RPA (cRPA) calculations is selected. The screening effects in the target space are calculated as follows
- [math]\displaystyle{ \tilde \chi^\sigma_{{\bf G,G}'}({\bf q},i\omega)\approx \frac 1{N_k}\sum_{nn'{\bf k}} \frac{ f_{n\bf k}-f_{n'\bf k-q} }{ \epsilon_{n{\bf k}} - \epsilon_{n'\bf k-q} - i \omega } \theta_{n\bf k }^{\sigma} \theta_{n'\bf k-p }^{\sigma'} \langle u_{n {\bf k }}^{\sigma } |e^{-i \bf (G+q) r}| u_{n'{\bf k-q}}^{ \sigma' } \rangle \langle u_{n' {\bf k-q}}^{\sigma' } |e^{-i \bf (G'-q)r'} | u_{n'{\bf k }}^{ \sigma } \rangle }[/math]
Here [math]\displaystyle{ \theta_{n{\bf k}}^\sigma }[/math] are the eigenvalues of the correlated projectors [math]\displaystyle{ P_{mn}^{\sigma({\bf k})} = \sum_{i\in \cal T} T_{i m}^{*\sigma({\bf k})} T_{i n}^{\sigma({\bf k})} }[/math] ordered according to their leverage scores. This method results in larger effective interactions compared to w-cRPA or the projector method and conserves the number of electrons.
Related tags and articles
LDISENTANGLED, LWEIGHTED, ALGO