triqs_tprf::dynamical_screened_interaction_W

#include <triqs_tprf.hpp>

Synopsis

  1. chi_wk_t dynamical_screened_interaction_W (chi_wk_cvt PI_wk, chi_k_cvt V_k)
  2. chi_fk_t dynamical_screened_interaction_W (chi_fk_cvt PI_fk, chi_k_cvt V_k)
  3. chi_wk_t dynamical_screened_interaction_W (chi_wk_cvt PI_wk, chi_wk_cvt V_wk)
  4. chi_fk_t dynamical_screened_interaction_W (chi_fk_cvt PI_fk, chi_fk_cvt V_fk)

Documentation

1) Dynamical screened interaction \(W(i\omega_n, \mathbf{k})\) calculator for static momentum-dependent bare interactions \(V(\mathbf{k})\).

The full screened interaction \(W(i\omega_n, \mathbf{k})\) is given by

\[W^{(full)}_{abcd}(i\omega_n, \mathbf{k}) = V_{abcd}(\mathbf{k}) + \sum_{efgh} V_{abef}(\mathbf{k}) \cdot \Pi_{fegh}(i\omega_n, \mathbf{k}) \cdot W^{(full)}_{hgcd}(i\omega_n, \mathbf{k})\]

2) Dynamical screened interaction \(W(\omega, \mathbf{k})\) calculator for static momentum-dependent bare interactions \(V(\mathbf{k})\).

The full screened interaction \(W(\omega, \mathbf{k})\) is given by

\[W^{(full)}_{abcd}(\omega, \mathbf{k}) = V_{abcd}(\mathbf{k}) + \sum_{efgh} V_{abef}(\mathbf{k}) \cdot \Pi_{fegh}(\omega, \mathbf{k}) \cdot W^{(full)}_{hgcd}(\omega, \mathbf{k})\]

3) Dynamical screened interaction \(W(i\omega_n, \mathbf{k})\) calculator for dynamic momentum-dependent bare interactions \(V(i\omega_n, \mathbf{k})\).

The full screened interaction \(W(i\omega_n, \mathbf{k})\) is given by

\[W^{(full)}_{abcd}(i\omega_n, \mathbf{k}) = V_{abcd}(i\omega_n, \mathbf{k}) + \sum_{efgh} V_{abef}(i\omega_n, \mathbf{k}) \cdot \Pi_{fegh}(i\omega_n, \mathbf{k}) \cdot W^{(full)}_{hgcd}(i\omega_n, \mathbf{k})\]

4) Dynamical screened interaction \(W(\omega, \mathbf{k})\) calculator for dynamic momentum-dependent bare interactions \(V(\omega, \mathbf{k})\).

The full screened interaction \(W(\omega, \mathbf{k})\) is given by

\[W^{(full)}_{abcd}(\omega, \mathbf{k}) = V_{abcd}(\omega, \mathbf{k}) + \sum_{efgh} V_{abef}(\omega, \mathbf{k}) \cdot \Pi_{fegh}(\omega, \mathbf{k}) \cdot W^{(full)}_{hgcd}(\omega, \mathbf{k})\]

Parameters

  • PI_wk polarization bubble \(\Pi_{abcd}(i\omega_n, \mathbf{k})\)

  • V_k static bare interaction \(V_{abcd}(\mathbf{k})\)

  • PI_fk polarization bubble \(\Pi_{abcd}(\omega, \mathbf{k})\)

  • V_wk dynamic bare interaction \(V_{abcd}(i\omega_n, \mathbf{k})\)

  • V_fk dynamic bare interaction \(V_{abcd}(\omega, \mathbf{k})\)

Returns

dynamical screened interaction \(W_{abcd}(i\omega_n, \mathbf{k})\)