solve_rpa_PH

Synopsis:

 triqs_tprf::chi_wk_t solve_rpa_PH (triqs_tprf::chi_wk_vt chi0,
array_view<std::complex<double>, 4> U)

Random Phase Approximation (RPA) in the particle-hole channel

Parameters

• chi0: bare particle-hole bubble \(\chi^{(0)}_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)\)
• U: RPA static vertex as obtained from triqs_tprf.rpa_tensor.get_rpa_tensor \(U_{a\bar{b}c\bar{d}}\)

Return value

RPA suceptibility \(\chi_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)\)

Documentation

Computes the equation

(1)\[\chi(\bar{a}b\bar{c}d) = \big( \mathbb{1} - \chi^{(0)}(\bar{a}b\bar{B}A) U(A\bar{B}D\bar{C}) \big)^{-1} \chi^{(0)}(\bar{C}D\bar{c}d)\,.\]