Haldane Honeycomb Lattice

Purpose and structure

The finite Haldane model has two honeycomb sublattices, real nearest-neighbor hopping $t_1$, oriented complex next-nearest-neighbor hopping $t_2e^{\pm i\phi}$, and staggered onsite potential $\pm M$.

Haldane honeycomb model

Basis and scaling

The single-particle dimension is $2N_rN_c$. Dense and CSR builders are available.

from quantum_lattice_models import haldane_honeycomb_lattice

H = haldane_honeycomb_lattice(
    n_rows=4, n_cols=4, t1=1.0, t2=0.18, phi=1.5708
)

Parameters

Builder	Parameter	Type	Default	Constraint
`haldane_honeycomb_lattice`	`n_rows`	`int`	`3`	>= 1
`haldane_honeycomb_lattice`	`n_cols`	`int`	`3`	>= 1
`haldane_honeycomb_lattice`	`t1`	`float`	`1.0`
`haldane_honeycomb_lattice`	`t2`	`float`	`0.18`
`haldane_honeycomb_lattice`	`phi`	`float`	`1.5707963267948966`
`haldane_honeycomb_lattice`	`sublattice_potential`	`float`	`0.0`
`haldane_honeycomb_lattice`	`periodic_x`	`bool`	`False`
`haldane_honeycomb_lattice`	`periodic_y`	`bool`	`False`
`haldane_honeycomb_lattice_sparse`	`n_rows`	`int`	`4`	>= 1
`haldane_honeycomb_lattice_sparse`	`n_cols`	`int`	`4`	>= 1
`haldane_honeycomb_lattice_sparse`	`t1`	`float`	`1.0`
`haldane_honeycomb_lattice_sparse`	`t2`	`float`	`0.18`
`haldane_honeycomb_lattice_sparse`	`phi`	`float`	`1.5707963267948966`
`haldane_honeycomb_lattice_sparse`	`sublattice_potential`	`float`	`0.0`
`haldane_honeycomb_lattice_sparse`	`periodic_x`	`bool`	`False`
`haldane_honeycomb_lattice_sparse`	`periodic_y`	`bool`	`False`

Validation and cautions

Complex next-nearest-neighbor phases and Hermitian conjugates are tested. Finite real-space spectra do not directly provide a Chern number; Bloch and topological-analysis support is planned.