[Wannier] Matrix elements of the Hamiltonian

[Robert Peyton Cline]

Dear Fhokrul,

In my experience with my own work (non spin-polarized CdS and CdSe
calculations), the Hamiltonian matrix elements are technically complex due
to small numerical imprecision.  My strongest elements might be order 1 eV
for the real part and order 10^-9 eV for the imaginary part.  While
technically complex, I think you would agree this value is basically real.
My weakest elements are perhaps 10^-9 eV for both the real and imaginary
parts, i.e. these elements are really basically 0.  I can't say how this
translates to your system, but in my experience for systems like mine (non
spin-polarized semiconductors), if the Wannier orbitals you get out are
mostly real, as they should be, then the Hamiltonian elements will be
mostly real as well.

You can check this by increasing the precision of the printed *hr.dat
file.  Or you can extract the unitary matrices U(k) from the *.chk file
(they are double precision in this file, 16 or 17 digits for each element)
and build your Hamiltonian from the DFT eigenvalues yourself in, say,
Matlab.

Best,
Peyton Cline
5th year PhD Student
Eaves Group
CU-Boulder

On Tue, May 26, 2020 at 2:44 AM Md. Fhokrul Islam <fislam at hotmail.com>
wrote:

> Dear developers and users,
>
> I have recently started to use Wannier90 code and I am wondering if
> someone can help me clarify some confusions.
>
> I am working with periodic systems. With spin-orbit coupling, the matrix
> elements of the Hamiltonian are, in general, expected to be complex except
> for the diagonal terms. But without spin-orbit, can the matrix element also
> be complex? Most of my calculations without spin-orbit show that the matrix
> elements are real. But one of my most recent calculations shows the
> elements are complex. So, I am wondering if it is correct or the result of
> some numerical error? In this case the system doesn't have inversion
> symmetry. Could it could be that since the DFT basis set are complex
> without inversion symmetry, and so the matrix elements of the Wannier90
> Hamiltonian are also complex?
>
> Also, is it possible to obtain complex matrix elements even with inversion
> symmetry and without spin-orbit coupling if disentanglement procedure is
> not done properly?
>
>
> Regards,
> Fhokrul
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