triqs_modest.local_gf
Local Green’s functions.
Compute the local Green’s function defined as:
\[[ G_{\mathrm{loc}}^{\sigma} ]_{m m'} = \sum_{\mathbf{k}} P_{m\nu}^{\sigma}(\mathbf{k}) \Big [ (\omega + \mu)\delta_{\nu\nu'} -
H^{\sigma}_{\nu\nu'}(\mathbf{k}) - [P_{m\nu}^{\sigma}]^{\dagger}\Sigma_{\mathrm{embed}}P_{m'\nu'}^{\sigma}(\mathbf{k}) \Big ]^{-1}
[P_{m'\nu'}^{\sigma}]^{\dagger},\]
where \(\omega\) is a frequency (either real- or Matsubra), \(\mu\) is the chemical potential, \(H(\mathbf{k})\) is the one-body Hamiltonian, \(P(\mathbf{k})\) are the projectors from the band to the orbital basis, and \(\Sigma_{\mathrm{embed}}\) is the embedded self-energy.
ModEST computes this efficiently:
Woodbury: reduces the cost of matrix inversion from cubic in the number of bands to linear.
Adaptive Brillouin zone integration: for tight-binding models, allows you to specify desired integration accuracy, improving predictions of transport properties.
Functions
Compute local Green's function on a \(M \times M\) mesh. |