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