Mixing Hamiltonian or Density Matrix?

[zhangguangping]

Dear all,

I have found that when we do NEGF self-consistent cycle, using mixing Hamiltonian most of the time will result in faster convergence. But this not all the story. When using mixing Hamiltonian at high bias, the convergence is very hard, the mixing Density Matrix can distinguish itself, mixing Density Matrix will get it converged.

My question is : What has actually happend in the above case? Mixing Hamiltonian or Density Matrix can result in the same convergence?

If both can lead to convergence, does it converge to the same point or on the same level?

Thanks you very much.

[Anders Blom]

That is very interesting, thanks for sharing your findings! Indeed, at high bias convergence gets tougher, and any trick that helps is useful to know.

There are never any guarantees with non-linear self-consistent loops, but I would be quite surprised if you ended up in very different places just because of the mixing scheme; after all, the Hamiltonian and density matrix are related, and the mixing method is "just" a numerical trick.

[zhangguangping]

Dear Anders Blom,

Thanks for your comments.

Since the Mixing Hamiltonian do not converge, so I can not tell whether they are converged to the same place.

What you have said mean once it converged whether using mixing Hamiltonian or Density matrix, it converge to the same level? That is to say, 1d-4 level for mixing Hamiltonian is also 1d-4 level for mixing Density?

Best regards

[Anders Blom]

It doesn't matter which variable you mix on, the convergence criterion is always the same. So in both cases you convert to the same accuracy, and most likely to the same (or very similar) state.