[Wannier] Unitary property of U^{dis}

[Hung Pham]

Hello Che-Hong,

I think it is possible that the U_dis matrix wasn't read and stored
properly. U and U_dis matrix must be unitary.
And the orthogonality of U_dis is always checked internally using the
*internal_check_orthonorm()* function in *disentangle.F90 *as Arash
mentioned.
I just included a function to read wannier90 U_matrices (either U_mat or
U_mat_opt) in my MCU <https://hungpham2017.github.io/mcu/index.html#>
package. Please see the function here
<https://github.com/hungpham2017/mcu/blob/master/mcu/wannier90/utils.py#L53>
.

The unitary of U or U_dis can be checked by using a simple python script:

import numpy as np
import mcu
kpts, U_kpts = mcu.read_U_matrix("wannier90_u_dis.mat")
nkpts, nband, nwann = U_kpts.shape
for i, kpt in enumerate(kpts):
    is_unitary = np.linalg.norm(U_kpts[i].T.conj() @ U_kpts[i] -
np.eye(nwann)) < 1.e-8
    print("kpt = {0:6.3f} {1:6.3f} {2:6.3f} ;Is U_kpt unitary?:
{3}".format(kpt[0], kpt[1], kpt[2], is_unitary))

I attached the in/out files from my testing on the MoS2 layer so you can
check it out yourself.
Let me know if it solves your problem.

Best,
Hung


On Tue, Mar 3, 2020 at 11:42 AM Mostofi, Arash <a.mostofi at imperial.ac.uk>
wrote:

> Dear Che-Hong
> I believe the code internally does this check (in subroutine dis_project
> in src/disentangle.F90) and reports an error if it is not satisfied.
> Admittedly, I’ve never explicitly checked that u_matrix_opt, as written to
> the seed name_u_dis.mat file, satisfies it... Note that the order of the
> matrix multiplication matters: U_{dis}^{\dagger}U_{dis} = 1, but not
> U_{dis}U_{dis}^{\dagger}, so a little care is needed in the evaluation.
> Perhaps you could check and, if you are sure it’s a problem, then post your
> input and output files (and script to read the matrices and evaluate the
> matrix product) and someone will try to take a look.
> Best wishes,
> Arash
>
> —
> Professor Arash Mostofi — www.mostofigroup.org
> Director, CDT in Theory and Simulation of Materials
> Imperial College London
>
>
>
>
> On 1 Mar 2020, at 14:00, 周哲弘 <lion08130716 at gmail.com> wrote:
>
> Dear Wannier developers
>
>
>
> I have used a combination of VASP (PAW-GGA package) and Wannier90 to obtain
>
> MLWFs in the system of monolayer MoS2.
>
>
>
> Recently I am trying to output the U and U^{dis} matrices (seedname_u.mat
> and seedname_u_dis.mat), and I find that U^{dis} doesn’t follow the rule
> (U^{dis})dagger* U^{dis}=1 (User Guide v3.0, p.14, footnote 2).
>
>
>
> Could anyone help me with this problem?
>
>
>
> Che-Hong Chou
>
> Graduate Student
>
> Department of Electrophysics
>
> National Chiao Tung University
>
> Taiwan
>
>
>
>
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-- 

Hung Q. Pham
Gagliardi Group
Office: Smith 101
Email: phamx494 at umn.edu
Personal page: hungpham2017.github.io
Department of Chemistry
University of Minnesota - Twin Cities, Minneapolis, MN 55455
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