triqs_tprf::lattice_dyson_g_wk

#include <triqs_tprf.hpp>

Synopsis

  1. g_wk_t lattice_dyson_g_wk (double mu, e_k_cvt e_k, g_w_cvt sigma_w)
  2. g_wk_t lattice_dyson_g_wk (double mu, e_k_cvt e_k, g_wk_cvt sigma_wk)
  3. g_Dwk_t lattice_dyson_g_wk (double mu, e_k_cvt e_k, g_Dwk_cvt sigma_wk)
  4. g_wk_t lattice_dyson_g_wk (double mu, e_k_cvt e_k, g_w_cvt sigma_w)
  5. g_Dwk_t lattice_dyson_g_wk (double mu, e_k_cvt e_k, g_Dw_cvt sigma_w)

Documentation

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

Computes

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

using a discretized dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\), chemical potential \(\mu\), and a momentum independent Matsubara frequency self energy \(\Sigma_{\bar{a}b}(i\omega_n)\).

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

Computes

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

using a discretized dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\), chemical potential \(\mu\), and a Matsubara frequency self energy \(\Sigma_{\bar{a}b}(i\omega_n, \mathbf{k})\).

3) Construct an interacting Matsubara frequency lattice Green’s function \(G_{a\bar{b}}(i\omega_n, \mathbf{k})\)

Computes

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

using a discretized dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\), chemical potential \(\mu\), and a Matsubara frequency self energy \(\Sigma_{\bar{a}b}(i\omega_n, \mathbf{k})\).

4) Construct an interacting Matsubara frequency lattice Green’s function \(G_{a\bar{b}}(i\omega_n, \mathbf{k})\)

Computes

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

using a discretized dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\), chemical potential \(\mu\), and a momentum independent Matsubara frequency self energy \(\Sigma_{\bar{a}b}(i\omega_n)\).

5) Construct an interacting Matsubara frequency lattice Green’s function \(G_{a\bar{b}}(i\omega_n, \mathbf{k})\)

Computes

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

using a discretized dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\), chemical potential \(\mu\), and a Matsubara frequency self energy \(\Sigma_{\bar{a}b}(i\omega_n)\).

Parameters

  • mu chemical potential \(\mu\)

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

  • sigma_w imaginary frequency self-energy \(\Sigma_{\bar{a}b}(i\omega_n)\)

  • sigma_wk imaginary frequency self-energy \(\Sigma_{\bar{a}b}(i\omega_n, \mathbf{k})\)

Returns

Matsubara frequency lattice Green’s function \(G_{a\bar{b}}(i\omega_n, \mathbf{k})\)