lattice_dyson_g_w

Synopsis:

 triqs_tprf::g_w_t lattice_dyson_g_w (double mu, triqs_tprf::e_k_cvt e_k,
triqs_tprf::g_w_cvt sigma_w)

Construct an interacting Matsubara frequency local (\(\mathbf{r}=\mathbf{0}\)) lattice Green’s function \(G_{a\bar{b}}(i\omega_n)\)

Parameters

• mu: chemical potential \(\mu\)
• e_k: discretized lattice dispersion \(\epsilon_{\bar{a}b}(\mathbf{k})\)
• sigma_w: imaginary frequency self-energy \(\Sigma_{\bar{a}b}(i\omega_n)\)

Return value

Matsubara frequency lattice Green’s function $G_{abar{b}}(iomega_n, mathbf{k})$

Documentation

Computes

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

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