Predefined Lattices

Predefined Lattices

Reference for the Bravais lattices available in ALF. These are implemented in Prog/Predefined_Latt_mod.F90 and selected via the Lattice_type string in the &VAR_lattice namelist.

Parameters

&VAR_lattice
L1 = 6
L2 = 6
Lattice_type = "Square"
Model = ""
/

• L1, L2 — lattice dimensions (number of unit cells in each direction)
• Lattice_type — string selecting the lattice (see table below)
• Model — optional model variant string (used by some Hamiltonians)

Available Lattices

Lattice_type	Orbitals per cell	Coord. vectors	Primitive vectors	Notes
"Square"	1	1 (1D) or 2 (2D)	$\mathbf{a}_1 = (1,0)$, $\mathbf{a}_2 = (0,1)$	Set L2=1 for a 1D chain
"N_leg_ladder"	L2	1	$\mathbf{a}_1 = (1,0)$	L2 orbitals per unit cell, L1 rungs; 1D geometry
"Bilayer_Square"	2	2	$\mathbf{a}_1 = (1,0)$, $\mathbf{a}_2 = (0,1)$	Two layers with 3D orbital positions
"Triangular"	1	3	$\mathbf{a}_1 = (1,0)$, $\mathbf{a}_2 = (1/2, \sqrt{3}/2)$	2D only (L1,L2 > 1)
"Honeycomb"	2	3	$\mathbf{a}_1 = (1,0)$, $\mathbf{a}_2 = (1/2, \sqrt{3}/2)$	A/B sublattice
"Bilayer_Honeycomb"	4	3	$\mathbf{a}_1 = (1,0)$, $\mathbf{a}_2 = (1/2, \sqrt{3}/2)$	Two honeycomb layers with 3D orbital positions
"Pi_Flux"	2	4	$\mathbf{a}_1 = (1,1)$, $\mathbf{a}_2 = (1,-1)$	2D only (L1,L2 > 1)
"Kagome"	3	4	$\mathbf{a}_1 = (1,0)$, $\mathbf{a}_2 = (1/2, \sqrt{3}/2)$	2D only (L1,L2 > 1)

The total number of orbitals is Ndim = L1 * L2 * Norb where Norb is the number of orbitals per unit cell.

Key Data Structures

After calling Predefined_Latt, the following are available:

Variable	Type	Description
Latt	Type(Lattice)	Bravais lattice: unit cell count N, neighbor list nnlist, distance map imj
Latt_unit	Type(Unit_cell)	Unit cell: Norb, coordination number N_coord, orbital positions Orb_pos_p
List(I,1)	Integer array	Unit cell index of site I
List(I,2)	Integer array	Orbital index of site I
Invlist(uc,orb)	Integer array	Site index of orbital orb in unit cell uc
Ndim	Integer	Total number of orbitals (Latt%N * Latt_unit%Norb)

Defining a Custom Lattice

If the predefined lattices don't fit your needs, you can define a custom lattice directly in your Hamiltonian's Ham_Set subroutine using the lattice library in Libraries/Modules/lattices_v3_mod.F90:

1. Create a Type(Unit_cell) specifying Norb, N_coord, orbital positions, and coordination vectors
2. Call Make_Lattice(Latt, Latt_unit, L1, L2) to build the full lattice
3. Construct the List/Invlist mapping arrays

See the existing Hamiltonians for examples of this pattern.