gftool.lattice.rectangular¶
2D rectangular lattice.
The dispersion of the 2D rectangular lattice is given by
\[ϵ_{k_x, k_y} = 2t [\cos(k_x) + γ\cos(k_y)]\]
where \(γ\) is the scale. The DOS has a singularity at \(2t(γ-1)=D(γ-1)/(γ+1)\).
| half_bandwidth: | The half-bandwidth D corresponds to a nearest neighbor hopping of t=D/2/(scale + 1) |
|---|---|
| scale: | Relative scale of the different hopping t_1 = scale*t_2. |
API¶
Functions
dos(eps, half_bandwidth, scale) |
DOS of non-interacting 2D rectangular lattice. |
gf_z(z, half_bandwidth, scale) |
Local Green’s function of the 2D rectangular lattice. |
hilbert_transform(xi, half_bandwidth, scale) |
Hilbert transform of non-interacting DOS of the rectangular lattice. |