triqs_tprf::construct_phi_wk
#include <triqs_tprf.hpp>
Synopsis
chi_wk_t construct_phi_wk (chi_wk_vt chi, array_contiguous_view<std::complex<double>, 4> U)
Computes reducible ladder vertex for the approximation of a local and static vertex.
In this approximation the reducible ladder vertex in density/magnetic channel are given by
\[\begin{split}\Phi^{\text{d/m}}_{a\overline{b}c\overline{d}}(Q) &\approx \frac{1}{(N_\mathbf{k}\beta)^2} \sum_{K'', K'''} U^{\text{d/m}}\chi^{\text{d/m}}(Q, K'', K''') U^{\text{d/m}} \\ &\approx U^{\mathrm{d/m}} \chi^{\text{d/m}}(Q) U^{\mathrm{d/m}}\,,\end{split}\]where all products are particle-hole products. The reducible ladder vertex in then only dependent on one bosonic frequency and momentum. It can then be used in
triqs_tprf.eliashberg.construct_gamma_singlet_rpa()ortriqs_tprf.eliashberg.construct_gamma__rpa()to construct the irreducible singlet/triplet vertex.
Parameters
chi density/magnetic susceptibility \(\chi^{\mathrm{d/m}}_{\bar{a}b\bar{c}d}(i\omega_n,\mathbf{q})\)
U density/magnetic local and static vertex \(U^{\mathrm{d/m}}_{a\bar{b}c\bar{d}}\)
Returns
The reducible ladder vertex in the density/magnetic channel \(\Phi^{\mathrm{d/m}}(i\omega_n,\mathbf{q})\)