lattice_dyson_g_wk

Synopsis:

 triqs_tprf::g_wk_t lattice_dyson_g_wk (double mu, triqs_tprf::e_k_cvt e_k,
triqs_tprf::g_w_cvt sigma_w)       (1)

 triqs_tprf::g_wk_t lattice_dyson_g_wk (double mu, triqs_tprf::e_k_cvt e_k,
triqs_tprf::g_wk_cvt sigma_wk)     (2)

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

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

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 \(G_{a\bar{b}}(i\omega_n, \mathbf{k})\)

Parameters

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

Return value

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

Documentation

Computes

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

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