triqs.dos.hilbert_transform.HilbertTransform

class triqs.dos.hilbert_transform.HilbertTransform(rho)[source]

Bases: object

Hilbert transform of a Green’s function against a density of states.

Computes the matrix-valued integral

\[\int_{-\infty}^{\infty} d\epsilon\, \rho(\epsilon) \Bigl[ (\omega + \mu + i\eta)\,\mathbf{1} - \hat\varepsilon(\epsilon) - \text{field} - \Sigma(\epsilon) \Bigr]^{-1}\]

on the mesh of a supplied Green’s function, given a DOS \(\rho\) and a self-energy \(\Sigma\).

Parameters:

rhoDOS: Density of states used as the integration weight. May be a plain DOS or a DOSFromFunction; the latter enables adaptive grid refinement via __call__().

Attributes

dos

(DOS) The DOS supplied at construction.

Methods

__call__(Sigma[, mu, eta, field, ...])

Evaluate the Hilbert transform with the given self-energy.