ASR for 1D system in the Hessian calculation

[lishouhang123456]

Dear developers and users,

I am working on the Hessian calculation for a 1D system. Considering the rotational symmetry constraints on 2nd-order force constants, there should be four acoustic phonon branches in this 1D system. I noticed that the Hessian dynamical matrices are related to the SSCHA dynamical phonon frequencies, according to Equations 21 and 22 in the paper （https://journals.aps.org/prb/pdf/10.1103/PhysRevB.96.014111）. Currently, SSCHA does not incorporate the rotational constraint, which means that it may introduce inaccuracies in the Hessian dynamical matrices due to errors in the SSCHA dynamical matrices, as shown below.

The red arrow in the plot marks the strong modification in the phonon dispersion due to the rotational symmetry constraint.

I have successfully modified the SSCHA code to incorporate the rotational symmetry constraint ('one-dim' in qe) into the SSCHA dynamical matrices. However, during the Hessian calculation, I encountered the following errors:

**ERROR WHILE UPDATING THE WEIGHTS

Error, one dynamical matrix does not satisfy the acoustic sum rule.
If this problem arises on a sscha run,
it may be due to a gradient that violates the sum rule.
Please, be sure you are not using a custom gradient function.

DETAILS OF ERROR:
Number of translatinal modes in the original dyn = 0
Number of translational modes in the target dyn = 3
(They should be both 3)**

I would like to know how to incorporate the rotational symmetry constraint in the Hessian calculation. Any suggestions on this issue would be greatly appreciated.

Best regards,
Shouhang