gftool.lattice
Collection of different lattices and their Green’s functions.
The lattices are described by a tight binding Hamiltonian
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
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 lattice with infinite coordination number. |
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Bethe lattice for general coordination number Z. |
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Green's function corresponding to a box DOS. |
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1D lattice. |
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2D square lattice. |
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2D rectangular lattice. |
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2D Lieb lattice. |
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2D triangular lattice. |
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2D honeycomb lattice. |
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2D Kagome lattice. |
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3D simple cubic (sc) lattice. |
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3D body-centered cubic (bcc) lattice. |
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3D face-centered cubic (fcc) lattice. |