Post-processing

Real-frequency spectral functions, projected spectral functions, and momentum-resolved spectral functions along high-symmetry paths.

Spectral functions

The projected spectral function on the correlated subspace \(\mathcal{C}\) is the imaginary part of the real-frequency local Green’s function,

\[A_{\mathcal{C}}^{\sigma}(\omega) = -\frac{1}{\pi}\, \mathrm{Im}\, \mathrm{Tr}_{\mathcal{C}}\, G_{\mathcal{C},\,\mathrm{loc}}^{\sigma}(\omega + i 0^{+}) = -\frac{1}{\pi}\, \mathrm{Im}\, \mathrm{Tr}_{\mathcal{C}} \sum_{\mathbf{k}} P(\mathbf{k})\, G_{\mathcal{B}}^{\sigma}(\mathbf{k}, \omega + i 0^{+})\, P^{\dagger}(\mathbf{k}),\]

and is reported either as a scalar trace or resolved by orbital \(m \in \mathcal{C}\) (diagonal entries \(A_{m}^{\sigma}(\omega)\)).

The momentum-resolved spectral function along a high-symmetry path \(\mathbf{k}(s)\) is the band-trace of the lattice Green’s function on the chosen path,

\[A^{\sigma}(\mathbf{k}(s), \omega) = -\frac{1}{\pi}\, \mathrm{Im}\, \mathrm{Tr}_{\nu}\, G_{\mathcal{B}}^{\sigma}(\mathbf{k}(s), \omega + i 0^{+}),\]

where \(G_{\mathcal{B}}^{\sigma}\) is evaluated on the high-symmetry path with the analytically-continued self-energy.

triqs_modest.post_processing.projected_spectral_function	Compute the atom- and orbital-resolved spectral function (interacting density of states).
triqs_modest.post_processing.spectral_function_on_high_symmetry_path	Compute momentum-resolved spectral function \(A^\sigma(k, \omega)\) along high-symmetry path.

Container types

triqs_modest.post_processing.SpectralFunctionW	Store data of spectral functions.
triqs_modest.post_processing.SpectralFunctionKw	Store data of spectral functions.