CUTOFF TYPE: Difference between revisions
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{{DISPLAYTITLE:CUTOFF_TYPE}} | {{DISPLAYTITLE:CUTOFF_TYPE}} | ||
{{TAGDEF|CUTOFF_TYPE|erfc {{!}} gaussian {{!}} fermi}} | {{TAGDEF|CUTOFF_TYPE|erfc {{!}} gaussian {{!}} fermi {{!}} num_wann}} | ||
{{DEF|CUTOFF_TYPE|erfc|}} | {{DEF|CUTOFF_TYPE|erfc|}} | ||
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This tag governs how much weight should be given in the | This tag governs how much weight should be given in the SVD during the [[Wannier_functions#One-shot_single_value_decomposition (SVD) | one-shot Wannierization]] to a certain orbital with energy <math>\epsilon_{n\mathbf{k}}</math>. | ||
If the weight is zero the orbital is not included in the fitting while if it is one it is included with the maximum importance. | If the weight is zero the orbital is not included in the fitting while if it is one it is included with the maximum importance. | ||
This behavior is similar to the wannier90 disentanglement window. | This behavior is similar to the wannier90 disentanglement window. | ||
In order to obtain a good Wannierization, a certain level of freedom should be given to the localized orbitals to adequately accommodate the Bloch states. This is particularly important for systems with entangled states. | In order to obtain a good Wannierization, a certain level of freedom should be given to the localized orbitals to adequately accommodate the Bloch states. | ||
Applying a smooth cutoff function from the following table can help achieve this goal by including more states beyond the relevant energy range. | |||
This is particularly important for systems with entangled states. | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
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| fermi || <math>\frac{1}{e^{(\epsilon_{n\mathbf{k}}-\mu)/\sigma}+1}</math> | | fermi || <math>\frac{1}{e^{(\epsilon_{n\mathbf{k}}-\mu)/\sigma}+1}</math> | ||
|} | |} | ||
with <math>\sigma</math> specified by the {{TAG|CUTOFF_SIGMA}} tag and <math>\mu</math> by {{TAG|CUTOFF_MU}}. | |||
In addition to the aforementioned cutoff functions, it is also possible to select {{TAGO|CUTOFF_TYPE|num_wann}}, which includes exactly as many Bloch states at each k-point as there are Wannier orbitals to be constructed. | |||
== Related tags and articles== | == Related tags and articles== | ||
{{TAG|CUTOFF_MU}}, | {{TAG|CUTOFF_MU}}, | ||
Latest revision as of 12:44, 27 June 2024
CUTOFF_TYPE = erfc | gaussian | fermi | num_wann
| Default: CUTOFF_TYPE | = erfc |
Description: CUTOFF_TYPE chooses the type of cutoff function to be used before performing the singular-value decomposition (SVD) of the initial projections matrix.
This tag governs how much weight should be given in the SVD during the one-shot Wannierization to a certain orbital with energy . If the weight is zero the orbital is not included in the fitting while if it is one it is included with the maximum importance. This behavior is similar to the wannier90 disentanglement window.
In order to obtain a good Wannierization, a certain level of freedom should be given to the localized orbitals to adequately accommodate the Bloch states. Applying a smooth cutoff function from the following table can help achieve this goal by including more states beyond the relevant energy range. This is particularly important for systems with entangled states.
| CUTOFF_TYPE | Function |
|---|---|
| erfc | |
| gaussian | |
| fermi |
with specified by the CUTOFF_SIGMA tag and by CUTOFF_MU.
In addition to the aforementioned cutoff functions, it is also possible to select CUTOFF_TYPE = num_wann, which includes exactly as many Bloch states at each k-point as there are Wannier orbitals to be constructed.