What is the physical origin of the difference between AUXILIARY and HESSIAN matrices?

[jgSi1113]

Dear all,

I performed a NPT calculation via SSCHA+QE and the minimization created a dynamical matrices, which should be the auxiliary SSCHA dynamical matrices used in arXiv:2411.03822v1. But very recently, I found there is another paper used the Hessian matrix to calculate the phonon dispersion. The later paper says "8 materials exhibit stable auxiliary SSCHA dynamical matrices, but their Hessian dynamical matrices still show imaginary frequencies..". What is the physical difference between the them? Which one is the more meaningful for the SSCHA calculations? [Although I think the later one is better.]

I have finshed the minimization and obtained the auxiliary SSCHA dynamical matrices, How can I transfer them into the Hessian ones?

Any suggestions and discussions will be greatly appreciated.

Thanks and Regards!
Jianguo Si

[DjordjeDangic]

To have a complete understanding of what are auxiliary and Hessian phonons please read these papers in detail: https://iopscience.iop.org/article/10.1088/1361-648X/ac066b/meta and https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.014111 .

However, in short, you can think of auxiliary phonons as the first correction to the harmonic phonons, while Hessian would be a second-order correction. One problem is that auxiliary phonons are always positive so they can not tell you anything about the dynamical stability of the system. If you want to see whether your system is dynamically stable (which is usually why one calculates phonons) you need to calculate free energy Hessian phonons.