triqs.gfs.descriptors.SemiCircular

class triqs.gfs.descriptors.SemiCircular(half_bandwidth, chem_potential=0.0)

Bases: Base

Hilbert transform of a semicircular density of states.

\[g(z) = \int \frac{A(\omega)}{z-\omega}\, d\omega, \qquad A(\omega) = \theta(D - |\omega|)\, \frac{2 \sqrt{D^2 - \omega^2}}{\pi D^2}.\]

Supports Matsubara, real-frequency and imaginary-time meshes.

Parameters:

half_bandwidthfloat

Half-bandwidth \(D\).

chem_potentialfloat, optional

Chemical potential \(\mu\), equal to minus the centre of the semicircle. Default 0.

Methods

__call__(G)

Fill G.data with the semicircular Hilbert transform on its mesh.

Examples

>>> from triqs.gfs import SemiCircular
>>> g << SemiCircular(half_bandwidth=1.0)