triqs_tprf::eliashberg_product

#include <triqs_tprf.hpp>

Synopsis

g_wk_t eliashberg_product (chi_wk_vt Gamma_pp, g_wk_vt g_wk, g_wk_vt delta_wk)

Linearized Eliashberg product via summation

Computes the linearized Eliashberg product in the singlet/triplet channel given by

\[\begin{split}\Delta^{\mathrm{s/t}, \mathrm{out}}_{\bar{a}\bar{b}}(i\nu,\mathbf{k}) = -\frac{1}{2N_\mathbf{k} \beta}\sum_{i\nu'}\sum_{\mathbf{k}'} \Gamma^{\mathrm{s/t}}_{c\bar{a}d\bar{b}}(i\nu - i\nu',\mathbf{k}-\mathbf{k}') \\ \times G_{c\bar{e}}(i\nu',\mathbf{k}') G_{d\bar{f}}(-i\nu',-\mathbf{k}') \Delta^{\mathrm{s/t}, \mathrm{in}}_{\bar{e}\bar{f}}(i\nu',\mathbf{k}')\,,\end{split}\]

by summation.

Parameters

• Gamma_pp particle-particle vertex \(\Gamma^{\mathrm{s/t}}_{a\bar{b}c\bar{d}}(i\nu_n,\mathbf{k})\)

• g_wk single particle Green’s function \(G_{a\bar{b}}(i\nu_n,\mathbf{k})\)

• delta_wk superconducting gap \(\Delta^{\mathrm{s/t}, \mathrm{in}}_{\bar{a}\bar{b}}(i\nu_n,\mathbf{k})\)

Returns

Gives the result of the product \(\Delta^{\mathrm{s/t}, \mathrm{out}}\)