LSCDM: Difference between revisions

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 $U_{mn\mathbf{k}}$ that transforms from the Bloch states $|\psi_{n\mathbf{k}}\rangle$ obtained by VASP to a Wannier basis $|w_{m\mathbf{R}}\rangle$ .

{\displaystyle |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. }

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 $\mu$ (CUTOFF_MU) and $\sigma$ (CUTOFF_SIGMA).

References

@@ Line 6: / Line 6: @@
 ----
-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

Revision as of 09:59, 20 July 2022

Related tags and articles

References