the density operators can be expanded in the basis of the single-particle electronic states
one easily obtains in the non-interacting picture
that in the non-interacting picture becomes
in yambo you can control the "type" of Green's function (causal or T-ordered) using the GrFnTp . The energy range is decided in EnRnge , while the damping is assumed linear in energy with bounds decided in DmRnge . The energy range is divided in ETStps uniform steps. Electron-hole pairs can be selected in energy using the EhEngy We have also introduced the oscillators matrix elements
The long-wavelength limit of the oscillators is easily calculated as
in this approximation the relation between the exact and the non interacting response function, in reciprocal space, is given by
(with repeated indexes summed).
In yambo input files the NGsBlk controls the size of the response
function in Reciprocal Space. Note that when NGsBlk = 1 no
Local Fields are considered. This corresponds to neglect the
charge oscillations induced by the external potential.
As mentioned before Eq.(2) can be solved either directly (a method that we will call G space ) or in the Bloch representation that rewrites Eq.(2) as an equation for the electron-hole Green's function (see BSK and TDDFT for more details).
In the general Many Body language, even if Eq.(2) is only approximated it defines the relation between the reducible and the irreducible response functions
with FT for Fourier Transform. This polarization function is much faster to calculate then the dynamical one and corresponds to a specific yambo runlevel.