### Response functions: the Plasmon-Pole approximation

The Plasmon-Pole runlevel yambo calculates an approximated and
fast expression for the screening function.
In the following discussion we consider only the symmetric frequency dependent part of the screening function (see also

GW ):

Consider the Lehman representation,

the PPA assumes that all the weight is given by a single excitation at the plasmon-pole frequency:

This approximation is justified since it has been observed that in general the Fourier
components are characterized by a strong peak at the plasmon pole frequency.
The variables in the calculations are analogous to those for the
response function ( Xd ): QpntsR decides
the momenta at which the response/screening is calculated; NGsBlk
decides the response/screening block-size; BndsRn
governes the band summation of the non-interacting response function;
EhEngy selects the energy of the hole-pairs in the electron-hole Green's
function. In the PPA yambo considers a casual Green's function.

#### Any logic in finding the plasmon-pole parameters?

The parameters of the PPA are determined by forcing the model to reproduce the dielectric matrix in the zero and plasmon-pole frequencies [2]:

where we understood all indexes for simplicity. From that one obtains:

The PPA imaginary energy Eo can be changed with PPAPnt .

#### References

- F. Aryasetiawan and O. Gunnarsson, Rep. Prog. Phys.
**61**, 237-312 (1998)
- R.W. Godby and R.J. Needs, Phys. Rev. Lett.
**62** 1169 (1989)