triqs_tprf::eliashberg_product

#include <triqs_tprf.hpp>

Synopsis

gk_iw_t eliashberg_product (chi_wk_vt Gamma_pp,

gk_iw_vt g_wk,

gk_iw_vt delta_wk)

Linearized Eliashberg product

Computes the product

(1)\[\Delta^{(out)}_{\bar{a}\bar{b}}(\mathbf{k},i\nu) = -\frac{1}{N_k \beta}\sum_{\mathbf{k}'} \sum_{i\nu'}\]

Gamma_{Abar{a}Bbar{b}}(mathbf{k}-mathbf{k}’, inu - inu’) \ times G_{Abar{c}}(mathbf{k}’, inu’) Delta_{bar{c}bar{d}}(mathbf{k}’, inu’) G_{Bbar{d}}(-mathbf{k}’, -inu’)

Parameters

• chi_pp particle-particle vertex \(\Gamma^{(pp)}_{a\bar{b}c\bar{d}}(\mathbf{k}, i\nu_n)\)
• g_kw single particle Green’s function \(G_{a\bar{b}}(\mathbf{k}, i\nu_n)\)
• delta_kw pairing self-energy \(\Delta_{\bar{a}\bar{b}}(\mathbf{k}, i\nu_n)\)

Returns

Gives the result of the product \(\Delta^{(out)} \sim \Gamma^{(pp)}GG \Delta\)