Fix acoustic_sum_rule computation in PhononBSDOSDoc

[hrushikesh-s]

The previous einsum('iijk->jk', fcs) summed only the on-site (i==j) self-interaction blocks, which is unrelated to the acoustic sum rule. The ASR condition is sum_j Phi_ij = 0 for every atom i.

Compute per-atom row sums and return the one with the largest Frobenius norm, so the field reports the worst per-atom violation.

Contributor Checklist

• I have broken down my PR scope into the following TODO tasks
  • Replace the on-site einsum with a per-atom row sum
• I have run the tests locally and they passed.
• I have added tests, or extended existing tests, to cover any new features or bugs fixed in this PR

[codecov-commenter]

Codecov Report

❌ Patch coverage is 11.53846% with 23 lines in your changes missing coverage. Please review.
✅ Project coverage is 85.56%. Comparing base (df5dc60) to head (0e5af9d).

Files with missing lines	Patch %	Lines
emmet-core/emmet/core/phonon.py	11.53%	23 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop    #1447      +/-   ##
===========================================
- Coverage    85.66%   85.56%   -0.10%     
===========================================
  Files          239      239              
  Lines        19167    19183      +16     
===========================================
- Hits         16419    16414       -5     
- Misses        2748     2769      +21     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[tsmathis]

seems okay to me, but I don't have the domain knowledge (Aaron, thoughts?)

[esoteric-ephemera]

@hrushikesh-s looking at ex this review, and using the notation that the ($q=0$) IFCs are N (# of atoms) x N x 3 x 3 tensors $C_{ij \alpha\beta}$, $i,j=1,2,...,N$ and $\alpha,\beta \in [1,2,3]$,

$$ \sum_j C_{ij \alpha\beta} = 0 $$

So perhaps the easiest checks of the ASR are:

np.abs(np.array(self.force_constants).sum(axis=1)).max() < thresh

with thresh some small number. Or even

np.all(np.abs(np.array(self.force_constants).sum(axis=1)) < thresh)

Thoughts?

[hrushikesh-s]

Thanks @esoteric-ephemera. I have now switched to np.abs(fcs.sum(axis=1)).max().
I have kept it as a raw scalar rather than < thresh so users can pick their own threshold and we keep quantitative info.

This new approach is also verified on mp-149, mp-189, mp-556120 --> all give ~1e-14, which is correct.
As a consequence, all three have the expected linear slopes for all of their acoustic modes near the Gamma-point, which is physically correct.

Looks good?

[tsmathis]

whichever method is decided on, it would be good if a citation/link (doi?) to the corresponding paper could be added that future develops can reference

[esoteric-ephemera]

Yep looks good to me, will add the citation now

[esoteric-ephemera]

@hrushikesh-s: I tweaked this a bit to return the N x 3 x 3 matrix from the ASR, since the same check on $max | \sum_j C_{ij\alpha \beta} |$ is done in check_sum_rule_deviations

@tsmathis removed the computed fields on a lot of these since I don't know that we need to save heavy arrays in memory. Thoughts?

[tsmathis]

I don't know that we need to save heavy arrays in memory

Yep that's reasonable. Merge whenever you're happy 👍
(and thanks for adding the references)