Wannier centers inconsistent with Wannier90 when 'guiding_centres' is used.

[greschd]

I've encountered a case where the Wannier centers computed by Wannier90 and wannier90-utils are inconsistent. Unfortunately I'm not allowed to share the input files[*], but the root cause is that in

wannier90-utils/src/w90utils/sprd.py

Line 19 in c22ae92

rv[i] = -1 * np.sum(bwv * np.imag(np.log(mii[:, i]))[:, np.newaxis], axis=0)

the np.imag(np.log(mii[:, i])) is well-defined only up to multiples of 2π.

This is the same "branch cut" problem that is worked around in Wannier90 by setting the guiding_centres=.true. option.

I'm not sure what the best approach would be here - do you think it would make sense to add a similar option that selects the closest Wannier center to a given "reference"?

[*] I'll try to come up with some other example that reproduces this behavior..

[jimustafa]

Hello @greschd. Thanks for reporting this issue. Yes, an option to specify "reference" centers, in order to fix the phases of the logarithm, seems like a reasonable approach. Been looking through the wann_phases routine in wannier90, but cannot quite understand how the phases are determined from the guiding centers. Presumably, for a set of centers, it is straightforward to compute the appropriate phases; and that this may differ from guiding_centres during the spread minimization.

[greschd]

I've also been looking at wann_phases, and didn't completely manage to parse it either. This e-mail thread from long ago helped somewhat: https://lists.quantum-espresso.org/pipermail/wannier/2013-November/000726.html

From what I understand so far:

• csum(i, b) = \sum_k M_{i,i}^{k, k+b} is used to obtain a "decent guess" for the average phase of the M_{i,i}^{k,k+b}s
• the first three (in b) xx(i, b) are chosen as -Im(log(csum(i, b))
• the other xx(i, b) are chosen to be close to b.rguide(i)
• that all is used somehow to update rguide(i).. I don't completely understand the logic there

This "updated" rguide is then used to compute sheet(i, b, k) = b.rguide(i), and csheet = e^{1j * sheet}.

The csheet and sheet are then used in other parts of Wannier90 (also when computing the spreads etc.).

I've played around with it a tiny bit, but haven't gotten to reproduce the same Wannier centers as Wannier90 yet.