[Wannier] Relative phases of converged Wannier orbitals

[Robert Peyton Cline]

Dear Wannier90 developers,

I have a question concerning the relative phases of the final Wannier
orbitals.  I've used Wannier90 for the past few years, and I feel quite
comfortable with the code and with how I've used it for my own research,
but I admit I am confused about one aspect of the final orbitals.  In the
Wannier90 papers, it is said that all of the final Wannier orbitals are
real up to a trivial global phase factor, assuming the global minimum is
reached.  In all of my simulations, I have verified this by plotting my
final MLWFs and investigating the maximum Im/Re values.  However, this
statement does not seem to exclude the possibility that the orbitals can
end up with opposite signs -- e.g. some phase-like prefactor, exp(-i*pi) =
-1.  I am wondering if something like this might happen because I am
currently doing some post-processing calculations where the sign of the
wavefunction might matter, i.e. by influencing the off-diagonal Hamiltonian
matrix elements.  On the one hand, I feel like the gauge transformation in
the multiband formalism alleviates this problem, but I am not entirely sure
if that's true.  Any help on this issue would be greatly appreciated.

Thank you,
Peyton Cline
4th year PhD student
Eaves Group
CU-Boulder
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