triqs_tprf::lattice_dyson_g_fk

#include <triqs_tprf.hpp>

Synopsis

  1. g_fk_t lattice_dyson_g_fk (double mu, e_k_cvt e_k, g_fk_cvt sigma_fk, double delta)
  2. g_fk_t lattice_dyson_g_fk (double mu, e_k_cvt e_k, g_f_cvt sigma_f, double delta)

Documentation

1) Construct an interacting real frequency lattice Green’s function \(G_{a\bar{b}}(\omega, \mathbf{k})\)

Computes

\[G_{a\bar{b}}(\omega, \mathbf{k}) = \left[ (\omega + i\delta + \mu ) \cdot \mathbf{1} - \epsilon(\mathbf{k}) - \Sigma(\omega, \mathbf{k}) \right]^{-1}_{a\bar{b}},\]

using a discretized dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\), chemical potential \(\mu\), broadening \(\delta\), and a real frequency self energy \(\Sigma_{\bar{a}b}(\omega, \mathbf{k})\).

2) Construct an interacting real frequency lattice Green’s function \(G_{a\bar{b}}(\omega, \mathbf{k})\)

Computes

\[G_{a\bar{b}}(\omega, \mathbf{k}) = \left[ (\omega + i\delta + \mu ) \cdot \mathbf{1} - \epsilon(\mathbf{k}) - \Sigma(\omega) \right]^{-1}_{a\bar{b}},\]

using a discretized dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\), chemical potential \(\mu\), broadening \(\delta\), and a real frequency self energy \(\Sigma_{\bar{a}b}(\omega)\).

Parameters

  • mu chemical potential \(\mu\)

  • e_k discretized lattice dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\)

  • sigma_fk real frequency self-energy \(\Sigma_{\bar{a}b}(\omega, \mathbf{k})\)

  • delta broadening \(\delta\)

Returns

real frequency lattice Green’s function \(G_{a\bar{b}}(\omega, \mathbf{k})\)