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### RPA spectral function

Posted: Tue Oct 09, 2018 5:59 am
Hi all,

I want to calculate k- and omega-dependent RPA spectral function (which is basically ARPES spectrum). Here k-points are chosen along the high-symmetry directions of the BZ (like in band structures)
Is it possible in Yambo? How to do it if it is possible?

Best,
Weiqing

### Re: RPA spectral function

Posted: Thu Oct 11, 2018 8:14 am
Dear Weiqing,

in ARPES you measure the bands, so the output of a GW calculation gives you the eigenvalues and also the related width (imaginary part of the self energy).
From that you can construct the ARPES signal in the QP approximation (i.e. only QP peaks available).
If you want to go beyond, you can set the Dyson solver to "g" in the input file for a GW calculation.
The output will be a frequency dependent spectral function for each band and each k-point.
There you would also get satellites, although probably not always in the right place, as discussed in recent works in the literature.
Is this what you mean when you write "RPA spectral function" ?

Hope it helps.
Best,
D.

### Re: RPA spectral function

Posted: Thu Oct 11, 2018 10:33 am
Dear Davide,

1. In GW calculation(with -g n), the output is
K-point Band Eo E E-Eo DFT HF Sc|Eo Sc|E dSc/dw|Eo Z(Re) Z(Im) Width[meV] Width[fs]
#
1.000 3.000 -.7424 -1.782 -1.040 -23.11 -28.94 4.561 4.783 -.2136 0.8240 -.1338E-2 17.75 37.08
1.000 4.000 -.7424 -1.820 -1.078 -23.11 -28.94 4.517 4.747 -.2134 0.8241 -.1335E-2 17.70 37.18
Actually, I don't understand the meaning of some column, f.e Sc|Eo, dSc/dw|Eo and Width.
Q1 : What is the meaning of them? And what is the definition of width?

2. Indeed, I can obtain the frequency-dependent Green's function in real-axis GW calculaton (-d -g g) and the output like :
Energy Re[G] |Im(G)| Re(S_tot) |Im(S_c)| Re(S_c)
-5.742438 -.4152761 0.3928327E-2 -2.592178 0.2277692E-1 3.230304
-5.742138 -.4153412 0.3929308E-2 -2.592256 0.2277546E-1 3.230226
Q2 : Is Re[G] the real part of Green's function (|Im(G)| for the Imaginary part )? And what is the meaning of Re(S_tot),|Im(S_c)| and Re(S_c)?

3. From Yambo Tutorials, I understand that PPA, COHSEX and real-aixs are implemented in GW calculation.
Q3 : can I do a GW calculation within Random Phase Approximation instead of PPA or COHSEX?

4. I want to do a GW calculation along a chosen k path, which is not uniform. From Tutorials, a new set of k-points containing chosen ones can be generated by BZ kpoint grid generator in ypp (ypp -k k). But when I add three new k-points into the list like:
%GWKpts # K points list
0.00000| 0.50000| 0.00000
0.00000| 0.48979| 0.00000
0.00000| 0.47959| 0.00000
%
Only the 3-rd point is in the new set of k-points.
Q4 : Can I generate a new set of k-points with more than one chosen point in ypp?

Best,
Weiqing

### Re: RPA spectral function

Posted: Fri Oct 12, 2018 4:40 pm
1. In GW calculation(with -g n), the output is
K-point Band Eo E E-Eo DFT HF Sc |Eo Sc|E dSc/dw|Eo
#
1.000 3.000 -.7424 -1.782 -1.040 -23.11 -28.94 4.561 4.783 -.2136
1.000 4.000 -.7424 -1.820 -1.078 -23.11 -28.94 4.517 4.747 -.2134 0.8241 -.1335E-2 17.70 37.18
Actually, I don't understand the meaning of some column, f.e Sc|Eo, dSc/dw|Eo and Width.
Q1 : What is the meaning of them? And what is the definition of width?

Width is the imaginary part of the self-energy
Z is the renormalization factor (you find the definition in MBPT books)
Sc is the real part of the correlation self-energy
The E or Eo in front I think depends it they are evaluated at the bare or at the QP pole(not sure)

2. Indeed, I can obtain the frequency-dependent Green's function in real-axis GW calculaton (-d -g g) and the output like :
Energy Re[G] |Im(G)| Re(S_tot) |Im(S_c)| Re(S_c)
-5.742438 -.4152761 0.3928327E-2 -2.592178 0.2277692E-1 3.230304
-5.742138 -.4153412 0.3929308E-2 -2.592256 0.2277546E-1 3.230226
Q2 : Is Re[G] the real part of Green's function (|Im(G)| for the Imaginary part )? And what is the meaning of Re(S_tot),|Im(S_c)| and Re(S_c)?

S_tot is the total self-energy, S_c the correlation part

3. From Yambo Tutorials, I understand that PPA, COHSEX and real-aixs are implemented in GW calculation.
Q3 : can I do a GW calculation within Random Phase Approximation instead of PPA or COHSEX?

If I undertand what you mean, RPA is what is yambo si called real-axis, i.e. byond PPA.
You do not put -p p nor -p c when generating the input

4. I want to do a GW calculation along a chosen k path, which is not uniform. From Tutorials, a new set of k-points containing chosen ones can be generated by BZ kpoint grid generator in ypp (ypp -k k). But when I add three new k-points into the list like:
%GWKpts # K points list
0.00000| 0.50000| 0.00000
0.00000| 0.48979| 0.00000
0.00000| 0.47959| 0.00000
%
Only the 3-rd point is in the new set of k-points.
Q4 : Can I generate a new set of k-points with more than one chosen point in ypp?

Yeah, you should be able.
I'm not ure hat is happening here.

Best,
D.