triqs_ctseg::evaluate_3w_vertex

#include <triqs_ctseg.hpp>

Synopsis

void evaluate_3w_vertex (block_gf<triqs::gfs::imfreq> const & gw,

block_gf<triqs::gfs::imfreq> const & fw,

gf_3w_container_t const & g3w,

gf_3w_container_t const & f3w,

bool measure_g3w,

bool measure_f3w,

std::string fname)

Evaluation of the 4-leg vertex for the 4-point correlation function

If one or two of the three-frequency correlation functions have been measured

and the parameter evaluate_vertex is set to true, the following vertex function is computed at the end of the simulation:

\[\gamma_{\sigma\sigma'}(i\omega,i\omega',i\nu) = \frac{G^{2,\text{con}}_{\sigma\sigma'}(i\omega,i\omega',i\nu)}{G_\sigma(i\omega)G_\sigma(i\omega+i\nu)G_\sigma'(i\omega'+i\nu)G_\sigma'(i\omega')}\]

Depending on which two-frequency correlation functions have been measured, the

connected part is computed in either of the following ways:

\[G^{2,\text{con}}_{\sigma}(i\omega,i\omega',i\nu) = G^{2}_{\sigma\sigma'}(i\omega,i\omega',i\nu) - G^{2,\text{disc}}_{\sigma\sigma'}(i\omega,i\omega',i\nu)\]

\[G^{2,\text{con}}_{\sigma}(i\omega,i\omega',i\nu) = G_\sigma(i\omega) F_{\sigma\sigma'}^{2}(i\omega,i\omega',i\nu)-F_\sigma(i\omega) G_{\sigma\sigma'}^{2}(i\omega,i\omega',i\nu)\]

\[G^{2,\text{con}}_{\sigma}(i\omega,i\omega',i\nu) = \Big[G_\sigma(i\omega) F_{\sigma\sigma'}^{2}(i\omega,i\omega',i\nu)-F_\sigma(i\omega) G_{\sigma}^{2,\text{disc}}(i\omega,i\omega',i\nu)\Big]/[1+F_\sigma(i\omega)].\]

The disconnected part of the correlation function has been defined as

\[G^{2,\text{disc}}_{\sigma\sigma'}(i\omega,i\omega',i\nu) = \beta G_{\sigma}(i\omega)G_\sigma'(i\omega')\delta_{\nu}-\beta G_\sigma(i\omega) G_\sigma(i\omega+i\nu)\delta_{\omega,\omega'}\delta_{\sigma\sigma'}.\]