Triangular-Lattice Tight Binding

Purpose and structure

The triangular lattice adds diagonal neighbors to the square-grid indexing, giving six bulk nearest neighbors and geometric frustration.

Finite lattice geometries

Basis and scaling

The single-particle dimension is $N_rN_c$. Dense and CSR builders are available, with independent periodic flags.

from quantum_lattice_models import triangular_lattice_tight_binding

H = triangular_lattice_tight_binding(n_rows=4, n_cols=5, hopping=1.0)

Parameters

Builder	Parameter	Type	Default	Constraint
`triangular_lattice_tight_binding`	`n_rows`	`int`	`3`	>= 1
`triangular_lattice_tight_binding`	`n_cols`	`int`	`3`	>= 1
`triangular_lattice_tight_binding`	`hopping`	`float`	`1.0`
`triangular_lattice_tight_binding`	`onsite`	`float`	`0.0`
`triangular_lattice_tight_binding`	`periodic_x`	`bool`	`False`
`triangular_lattice_tight_binding`	`periodic_y`	`bool`	`False`
`triangular_lattice_tight_binding_sparse`	`n_rows`	`int`	`8`	>= 1
`triangular_lattice_tight_binding_sparse`	`n_cols`	`int`	`8`	>= 1
`triangular_lattice_tight_binding_sparse`	`hopping`	`float`	`1.0`
`triangular_lattice_tight_binding_sparse`	`onsite`	`float`	`0.0`
`triangular_lattice_tight_binding_sparse`	`periodic_x`	`bool`	`False`
`triangular_lattice_tight_binding_sparse`	`periodic_y`	`bool`	`False`

User notes

Use triangular_lattice_positions for geometry-aware plotting. Small periodic dimensions may cause multiple geometric bonds to connect the same pair; matrix entries accumulate those contributions.