gftool.lattice.bethe.gf_z_inv¶

gftool.lattice.bethe.gf_z_inv(gf, half_bandwidth)[source]¶

Inverse of local Green’s function of Bethe lattice for infinite coordination number.

\[R(G) = (D/2)^2 G + 1/G\]

where \(R(z) = G^{-1}(z)\) is the inverse of the Green’s function.

Parameters

gfcomplex array_like or complex: Value of the local Green’s function.
half_bandwidthfloat: Half-bandwidth of the DOS of the Bethe lattice. The half_bandwidth corresponds to the nearest neighbor hopping t=D/2

Returns

zcomplex np.ndarray or complex: The inverse of the Bethe Green’s function gf_z(gf_z_inv(g, D), D)=g.

See also

gftool.lattice.bethe.gf_z

References

georges1996: Georges et al., Rev. Mod. Phys. 68, 13 (1996) https://doi.org/10.1103/RevModPhys.68.13

Examples

>>> ww = np.linspace(-1.5, 1.5, num=500) + 1e-4j
>>> gf_ww = gt.lattice.bethe.gf_z(ww, half_bandwidth=1)
>>> np.allclose(ww, gt.lattice.bethe.gf_z_inv(gf_ww, half_bandwidth=1))
True