gftool.bethe_hilbert_transform
- gftool.bethe_hilbert_transform(xi, half_bandwidth)
Hilbert transform of non-interacting DOS of the Bethe lattice.
The Hilbert transform is defined as:
\[\tilde{D}(ξ) = ∫_{-∞}^{∞}dϵ \frac{DOS(ϵ)}{ξ − ϵ}\]The lattice Hilbert transform is the same as the non-interacting Green’s function.
- Parameters:
- xicomplex array_like or complex
Point at which the Hilbert transform is evaluated.
- half_bandwidthfloat
Half-bandwidth of the DOS of the Bethe lattice.
- Returns:
- complex np.ndarray or complex
Hilbert transform of xi.
See also
Notes
Relation between nearest neighbor hopping t and half-bandwidth D:
\[2t = D\]