LSCRPA: Difference between revisions
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{{TAGDEF|LSCRPA|[logical]|.FALSE.}} | {{TAGDEF|LSCRPA|[logical]|.FALSE.}} | ||
Description: {{TAG|LSCRPA}} selects the [[Constrained–random-phase–approximation_formalism#Spectral-cRPA_method_(s-cRPA)|spectral-cRPA method]]. | Description: {{TAG|LSCRPA}} selects the [[Constrained–random-phase–approximation_formalism#Spectral-cRPA_method_(s-cRPA)|spectral-cRPA method]]. | ||
{{Available|6.6.0}} | {{Available|6.6.0}} | ||
In constrained random-phase approximation (cRPA) calculations, the target polarizability <math>\tilde\chi</math> is computed from the eigenspectrum of the target-space projectors as follows | In constrained random-phase approximation (cRPA) calculations, the target polarizability <math>\tilde\chi</math> is computed from the eigenspectrum of the target-space projectors 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 | ||
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ordered according to their leverage scores. The s-cRPA method results in larger effective interactions compared to [[Constrained–random-phase–approximation_formalism#Weighted-cRPA_method_(w-cRPA)|w-cRPA]] or the [[Constrained–random-phase–approximation_formalism#Projector-cRPA_method_(p-cRPA)|projector-cRPA method]] and conserves the number of electrons.{{cite|kaltak:prb:2025}} | ordered according to their leverage scores. The s-cRPA method results in larger effective interactions compared to [[Constrained–random-phase–approximation_formalism#Weighted-cRPA_method_(w-cRPA)|w-cRPA]] or the [[Constrained–random-phase–approximation_formalism#Projector-cRPA_method_(p-cRPA)|projector-cRPA method]] and conserves the number of electrons.{{cite|kaltak:prb:2025}} | ||
== Related tags and articles == | == Related tags and articles == | ||
{{TAG|LDISENTANGLED}}, | {{TAG|LDISENTANGLED}}, | ||
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{{TAG|ALGO}} | {{TAG|ALGO}} | ||
{{sc|LSCRPA| | {{sc|LSCRPA|Howto|Workflows that use this tag}} | ||
== References == | == References == | ||
Latest revision as of 09:37, 20 March 2026
LSCRPA = [logical]
Default: LSCRPA = .FALSE.
Description: LSCRPA selects the spectral-cRPA method.
| Mind: Available as of VASP 6.6.0 |
In constrained random-phase approximation (cRPA) calculations, the target polarizability [math]\displaystyle{ \tilde\chi }[/math] is computed from the eigenspectrum of the target-space projectors 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. The s-cRPA method results in larger effective interactions compared to w-cRPA or the projector-cRPA method and conserves the number of electrons.[1]
Related tags and articles
LDISENTANGLED, LWEIGHTED, ALGO