eliashberg_product

Synopsis:

 triqs_tprf::gk_iw_t eliashberg_product (triqs_tprf::chi_wk_vt Gamma_pp,
triqs_tprf::gk_iw_vt g_wk, triqs_tprf::gk_iw_vt delta_wk)

Linearized Eliashberg product

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 \(\Delta_{\bar{a}\bar{b}}(\mathbf{k}, i\nu_n)\)

Return value

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

Documentation

Computes the product

(1)\[\begin{split}\Delta^{(out)}_{\bar{a}\bar{b}}(\mathbf{k},i\nu) = -\frac{1}{N_k \beta}\sum_{\mathbf{k}'} \sum_{i\nu'} \Gamma_{A\bar{a}B\bar{b}}(\mathbf{k}-\mathbf{k}', i\nu - i\nu') \\ \times G_{A\bar{c}}(\mathbf{k}', i\nu') \Delta_{\bar{c}\bar{d}}(\mathbf{k}', i\nu') G_{B\bar{d}}(-\mathbf{k}', -i\nu')\end{split}\]