triqs_tprf::solve_rpa_PH

#include <triqs_tprf.hpp>

Synopsis

1. chi_wk_t solve_rpa_PH (chi_wk_vt chi0, array_contiguous_view<std::complex<double>, 4> U)
2. chi_fk_t solve_rpa_PH (chi_fk_vt chi0, array_contiguous_view<std::complex<double>, 4> U)

Documentation

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

Computes the equation

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

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

Computes the equation

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

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 \(U_{a\bar{b}c\bar{d}}\)

Returns

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