chi0q_from_g_wk_PH

Synopsis:

triqs_tprf::chi_wnk_t chi0q_from_g_wk_PH (int nw, int nn, triqs_tprf::g_wk_cvt g_wk)

Generalized susceptibility bubble in the particle-hole channel \(\chi^{(0)}_{\bar{a}b\bar{c}d}(\omega, \nu, \mathbf{q})\) with convolution in k-space.

Parameters

• nw: Number of bosonic Matsubara freqiencies.
• nn: Number of fermionic Matsubara freqiencies.
• g_tr: Imaginary time Green’s function in real-space, \(G_{a\bar{b}}(\nu, \mathbf{r})\).

Return value

Generalized susceptibility \(\chi^{(0)}_{\bar{a}b\bar{c}d}(\omega, \nu, \mathbf{r})\) in one bosonic and one fermionic Matsuabara frequency and real-space.

Documentation

Computes

(1)\[\chi^{(0)}_{\bar{a}b\bar{c}d}(\omega, \nu, \mathbf{q}) = - \frac{\beta}{N_k} \sum_\mathbf{k} G_{d\bar{a}}(\nu, \mathbf{k}) \cdot G_{b\bar{c}}(\nu + \omega, \mathbf{k} - \mathbf{q})\]