LSCDM: Difference between revisions

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The selected columns of the density matrix {{TAG|LSCDM}} method works by fitting a unitary matrix <math>U_{mn\mathbf{k}}</math> that transforms from the Bloch states obtained by VASP to a [[Wannier functions| Wannier basis]].
The selected columns of the density matrix (SCDM) method works by fitting a unitary matrix <math>U_{mn\mathbf{k}}</math> that transforms  
The SCDM method is implemented as proposed by A. Dale and L. Lin {{cite|dale:mms:2018}}.
from the Bloch states <math>|\psi_{n\mathbf{k}}\rangle</math> obtained by VASP to a [[Wannier functions| Wannier basis]] <math>|w_{m\mathbf{R}}\rangle</math>.
This is done using a [[Wannier_Functions#One-shot_single_value_decomposition (SVD) | one-shot method ]] through a singular-value decomposition (SVD).
 
::<math>
|w_{m\mathbf{R}}\rangle =
\sum_{n\mathbf{k}}
e^{-i\mathbf{k}\cdot\mathbf{R}}
U_{mn\mathbf{k}}
|\psi_{n\mathbf{k}}\rangle.
</math>
 
This is done using a [[Wannier_Functions#One-shot_single_value_decomposition (SVD) | one-shot method ]] through a singular-value decomposition as proposed by A. Dale and L. Lin {{cite|dale:mms:2018}}.


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 controlled by the cutoff function specified by the {{TAG|CUTOFF_TYPE}} tag and related parameters  
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 controlled by the cutoff function specified by the {{TAG|CUTOFF_TYPE}} tag and related parameters  

Revision as of 09:59, 20 July 2022

LSCDM = .TRUE. | .FALSE. 

Default: LSCDM = .FALSE.

Description: LSCDM switches on the selected columns of the density matrix (SCDM) method.


The selected columns of the density matrix (SCDM) method works by fitting a unitary matrix that transforms from the Bloch states obtained by VASP to a Wannier basis .

This is done using a one-shot method through a singular-value decomposition as proposed by A. Dale and L. Lin .

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 controlled by the cutoff function specified by the CUTOFF_TYPE tag and related parameters (CUTOFF_MU) and (CUTOFF_SIGMA).

Related tags and articles

CUTOFF_TYPE, CUTOFF_MU, CUTOFF_SIGMA

Examples that use this tag

References