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.