Kagome-Lattice Tight Binding
Purpose and structure
The kagome lattice has three sublattice sites per unit cell and triangular connectivity. It is a standard flat-band and frustrated-lattice testbed.
Basis and scaling
The single-particle dimension is $3N_rN_c$. Dense and CSR builders are available.
from quantum_lattice_models import kagome_lattice_tight_binding_sparse
H = kagome_lattice_tight_binding_sparse(n_rows=4, n_cols=4)
Parameters
| Builder | Parameter | Type | Default | Constraint |
|---|---|---|---|---|
kagome_lattice_tight_binding |
n_rows |
int |
2 |
>= 1 |
kagome_lattice_tight_binding |
n_cols |
int |
3 |
>= 1 |
kagome_lattice_tight_binding |
hopping |
float |
1.0 |
|
kagome_lattice_tight_binding |
onsite |
float |
0.0 |
|
kagome_lattice_tight_binding |
periodic_x |
bool |
False |
|
kagome_lattice_tight_binding |
periodic_y |
bool |
False |
|
kagome_lattice_tight_binding_sparse |
n_rows |
int |
4 |
>= 1 |
kagome_lattice_tight_binding_sparse |
n_cols |
int |
4 |
>= 1 |
kagome_lattice_tight_binding_sparse |
hopping |
float |
1.0 |
|
kagome_lattice_tight_binding_sparse |
onsite |
float |
0.0 |
|
kagome_lattice_tight_binding_sparse |
periodic_x |
bool |
False |
|
kagome_lattice_tight_binding_sparse |
periodic_y |
bool |
False |
User notes
Use kagome_lattice_positions and kagome_lattice_index for plotting and
indexing. Sublattice labels are not automatically attached to sparse matrices.