triqs_tprf::gamma_PP_triplet

#include <triqs_tprf.hpp>

Synopsis

chi_wk_t gamma_PP_triplet (chi_wk_vt chi_c,

chi_wk_vt chi_s,

array_view<std::complex<double>, 4> U_c,

array_view<std::complex<double>, 4> U_s)

Gamma particle-particle triplet

Computes the particle-particle vertex for triplet pairing in the RPA limit

(1)\[\begin{split}\Gamma^{(\mathrm{triplet})}(a\bar{b}c\bar{d}) = -\frac{1}{2} U^{(\mathrm{s})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{s})}(\bar{B}A\bar{C}D) U^{(\mathrm{s})}(D\bar{C}c\bar{d}) \\ -\frac{1}{2} U^{(\mathrm{c})}(a\bar{b}A\bar{B}) \chi^{(\mathrm{c})}(\bar{B}A\bar{C}D) U^{(\mathrm{c})}(D\bar{C}c\bar{d}) \\ + \frac{1}{2}\big(U^{(\mathrm{s})}(a\bar{b}c\bar{d})+ U^{(\mathrm{c})}(a\bar{b}c\bar{d})\big)\end{split}\]

Parameters

• chi_c charge susceptibility \(\chi^{(\mathrm{c})}_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)\)
• chi_s spin susceptibility \(\chi^{(\mathrm{s})}_{\bar{a}b\bar{c}d}(\mathbf{k}, i\omega_n)\)
• U_c charge interaction \(U^{(\mathrm{c})}_{a\bar{b}c\bar{d}}\)
• U_s spin interaction \(U^{(\mathrm{s})}_{a\bar{b}c\bar{d}}\)

Returns

\(\Gamma^{(\mathrm{triplet})}_{a\bar{b}c\bar{d}}(\mathbf{k}, i\omega_n)\)