gftool.lattice¶
Collection of different lattices and their Green’s functions.
The lattices are described by a tight binding Hamiltonian
\[H = t ∑_{⟨i,j⟩ σ} c^†_{iσ} c_{jσ},\]
where \(t\) is the hopping amplitude or integral. Mind the sign, often tight binding Hamiltonians are instead defined with a negative sign in front of \(t\).
The Hamiltonian can be diagonalized
\[H = ∑_{kσ} ϵ_{k} c^†_{kσ} c_{kσ}.\]
Typical quantities provided for the different lattices are:
| gf_z: | The one-particle Green’s function
\[G_{ii}(z) = ⟨⟨c_{iσ}|c^†_{iσ}⟩⟩(z) = 1/N ∑_k \frac{1}{z - ϵ_k}.\]
|
|---|---|
| dos: | The density of states (DOS)
\[DOS(ϵ) = 1/N ∑_k δ(ϵ - ϵₖ).\]
|
| dos_moment: | The moments of the DOS
\[ϵ^{(m)} = ∫dϵ DOS(ϵ) ϵ^m\]
|
Submodules¶
bethe |
Bethe lattice with infinite coordination number. |
bethez |
Bethe lattice for general coordination number Z. |
onedim |
1D lattice. |
square |
2D square lattice. |
rectangular |
2D rectangular lattice. |
lieb |
2D Lieb lattice. |
triangular |
2D triangular lattice. |
honeycomb |
2D honeycomb lattice. |
kagome |
2D Kagome lattice. |
sc |
3D simple cubic (sc) lattice. |
bcc |
3D body-centered cubic (bcc) lattice. |
fcc |
3D face-centered cubic (fcc) lattice. |