Custom Lattice and Tight Binding

Purpose and structure

Lattice, LatticeSpec, and TightBindingModel support finite user-defined graphs with coordinates, complex bonds, labels, unit cells, boundary metadata, and onsite terms.

Two-item bonds (i, j) use -hopping. Three-item bonds (i, j, value) use value directly. With hermitian=True, the conjugate reverse matrix element is added automatically.

Package use

from quantum_lattice_models import Lattice, TightBindingModel

lattice = Lattice(
    positions=[(0, 0), (1, 0), (0.5, 0.8)],
    bonds=[(0, 1), (1, 2, 0.25j), (2, 0)],
)
H = TightBindingModel(lattice).hamiltonian(hopping=1.0)

quantum-lattice create custom_tight_binding \
  --n-sites 3 --bond 0,1 --bond 1,2,0.25j --output custom.json

Parameters

Builder	Parameter	Type	Default	Constraint
`custom_tight_binding`	`n_sites`	`int`	`3`	>= 1
`custom_tight_binding`	`bonds`	`str`	`((0, 1), (1, 2))`
`custom_tight_binding`	`hopping`	`complex`	`1.0`
`custom_tight_binding`	`onsite`	`float`	`0.0`
`custom_tight_binding`	`hermitian`	`bool`	`True`
`custom_tight_binding_sparse`	`n_sites`	`int`	`16`	>= 1
`custom_tight_binding_sparse`	`bonds`	`str`	`((0, 1), (1, 2))`
`custom_tight_binding_sparse`	`hopping`	`complex`	`1.0`
`custom_tight_binding_sparse`	`onsite`	`float`	`0.0`
`custom_tight_binding_sparse`	`hermitian`	`bool`	`True`

Validation and cautions

Bond indices, coordinate dimensions, and dense/sparse agreement are tested. Set hermitian=False only when a directed or explicitly non-Hermitian model is intended.