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.

API