Does Z2pack enforce any symmetries when calculating Berry phases?

[jkidd1]

Hi Dominik,

I am studying a 1D chain model that I have loaded in from a VASP calculation using Wannier90 and tbmodels. The chain has 2 sites in the unit cell and has inversion symmetry, with inversion centered on either of the sites. However, when I solve for the ground state using DFT, I find that this symmetry is spontaneously broken, i.e., the hopping from site 1 in cell 1 to site 2 in cell 1 is not the same as the hopping from site 1 in cell 1 to site 2 in cell 0. Hopefully this makes sense, but if it is not clear, I can try to elaborate. Anyway, I then calculated the Zak phase with Z2Pack and found it to be quantized, even with the broken symmetry. This was surprising to me, as I would expect it to be continuous. I was wondering if there is some part of tbmodels, for example, that is restoring the inversion symmetry. I read that tbmodels has a "symmetrization" feature, but I am not sure what that entails. Do you have any suggestions?

Thanks,
Jamin

[greschd]

Hi Jamin,

No, in general Z2Pack doesn't enforce symmetries. The symmetrization feature in TBmodels also needs to be explicitly called, so that shouldn't have an impact here. It simply deletes the non-symmetric part of the hopping matrices, so is only useful when the model is "almost" symmetric to enforce degeneracies, not when far away from a symmetric case.

Now, to speculate what might be happening here: The Wannier90 process roughly consists of two steps:

• Disentanglement: here, the model is "cut off", to represent an isolated set of bands. This potentially changes the model physically.
• Maximal localization: this simply changes the basis functions to the maximally localized ones. In principle (excluding numerical inaccuracies), this should not physically change the model. Since it "mixes" the original (projected) basis, the resulting basis functions are no longer necessarily symmetric. When taking into account the shape of the basis functions however, it should still be symmetric -- as long as it was symmetric at the start of the maximal localization procedure. Another way of thinking about this is that the representation of inversion symmetry has become more complicated in the new basis.

That could be what is happening in your model, and would explain why the Zak phase still respects the symmetry.

Some things to check would be:

• does the band structure also shows gaps opening where degeneracies would be enforced by inversion symmetry?
• what happens when disabling the maximal localization procedure (setting the number of steps to 0) in Wannier90?