Square-Lattice Tight Binding

Purpose and structure

This model places one orbital at each site of an $N_r\times N_c$ rectangular grid with row-major indexing and nearest-neighbor hopping.

Finite lattice geometries

Basis and scaling

The single-particle dimension is $N_rN_c$. Dense and CSR builders are available. Opposite edges can be reconnected independently along $x$ and $y$.

from quantum_lattice_models import square_lattice_tight_binding_sparse

H = square_lattice_tight_binding_sparse(
    n_rows=20, n_cols=20, periodic_x=True
)

Parameters

Builder	Parameter	Type	Default	Constraint
`square_lattice_tight_binding`	`n_rows`	`int`	`3`	>= 1
`square_lattice_tight_binding`	`n_cols`	`int`	`4`	>= 1
`square_lattice_tight_binding`	`hopping`	`float`	`1.0`
`square_lattice_tight_binding`	`onsite`	`float`	`0.0`
`square_lattice_tight_binding`	`periodic_x`	`bool`	`False`
`square_lattice_tight_binding`	`periodic_y`	`bool`	`False`
`square_lattice_tight_binding_sparse`	`n_rows`	`int`	`8`	>= 1
`square_lattice_tight_binding_sparse`	`n_cols`	`int`	`8`	>= 1
`square_lattice_tight_binding_sparse`	`hopping`	`float`	`1.0`
`square_lattice_tight_binding_sparse`	`onsite`	`float`	`0.0`
`square_lattice_tight_binding_sparse`	`periodic_x`	`bool`	`False`
`square_lattice_tight_binding_sparse`	`periodic_y`	`bool`	`False`

User notes

Use square_lattice_positions for plotting. This model has real hopping and no magnetic flux; use Harper-Hofstadter for Peierls phases.