Transforming from imaginary time to imaginary frequency domain

[bprobinson102]

Dear VASP team,

I am wanting to obtain the frequency-dependent self-energies from a low-scaling GW calculation at finite temperature. I am following the procedure from this paper:https://journals.aps.org/prb/abstract/1 ... .94.165109 . However, I am confused which transformation matrix from the OUTCAR to use, since there are eight of them in total. If this could be clarified that would be great.

Best,
Brian Robinson

[merzuk.kaltak]

Dear Brian,

since you have set LFINIT_TEMPERATURE, you might want to study PhysRevB.101.205145.
In summary there are four transformations for a transform from one grid to another grid. This comes from the fact that the matrix is first split into
symmetric and anti-symmetric part and each part has an own transformation to cosine and sine grid, respectively.
Furthermore, there are two grids in frequency domain, an optimal cosine and an optimal sine grid.

[merzuk.kaltak]

Maybe another comment is in place here,

since the self-energy is a fermionic quantity, the fermionic frequency gird, described in PhysRevB.101.205145, is used and printed to vasprun.xml, if one sets LSELFENERGY=T in the INCAR.
An example output would read like the following

Code: Select all

<varray name="selfenergy along imaginary axis" >                                                                                                                                                                                                                          
  <v>       0.1570801806644298    -23.7971327349915711     -0.0179645094529067</v>                                                                                                                                                                                         
  <v>       0.4718033117773284    -23.7968260788831572     -0.0537856829291801</v>                                                                                                                                                                                         
  <v>       0.8108804505648752    -23.7966749072893577     -0.0932103588740998</v>                                                                                                                                                                                         
  <v>       1.3058951128526406    -23.7949927690568188     -0.1482973553314607</v>         
...

Here the first column corresponds to the imaginary frequency point (of the fermionic grid), while the second and third column are the real and imaginary part of the self-energy.