build_heisenberg¶

Populate interactions for a Heisenberg spin model.

build_heisenberg ¶

build_heisenberg(
    interactions: List[Interaction],
    L: int = 0,
    *,
    symmetry: str = "U1",
    spin: float = 0.5,
    J: float = 1.0,
    Jp: float = 0.0,
    space_fn: Optional[Callable] = None,
    **_ignored,
) -> Tuple[Index, Dict[str, Tensor]]

Populate interactions for a Heisenberg spin model.

Assigns the spin-spin coupling J S†_i · S_j to each NN bond and Jp S†_i · S_j to each NNN bond. Tensors are built from build_bosonic (or space_fn if provided) and stored without baking in the coupling; build_hamiltonian applies intr.cpl when constructing the MPO.

Parameters:

Name	Type	Description	Default
`interactions`	`List[Interaction]`	List of `Interaction2Site` objects from the geometry stage. Modified in place.	required
`L`	`int`	Chain length. Unused here (present for uniform model-builder API).	`0`
`symmetry`	`str`	Symmetry passed to `build_bosonic` — `'U1'` or `'SU2'`.	`'U1'`
`spin`	`float`	Site spin quantum number.	`0.5`
`J`	`float`	Coupling for NN bonds (label `'NN'`).	`1.0`
`Jp`	`float`	Coupling for NNN bonds (label `'NNN'`). Interactions with `Jp == 0` are left with `cpl = 0.0` and no tensors; `build_hamiltonian` skips them.	`0.0`
`space_fn`	`Optional[Callable]`	Optional replacement for `build_bosonic`. Must have the same signature: `space_fn(symmetry, spin) -> (spc, ops)`.	`None`
`**_ignored`		Extra TOML keys forwarded from the dispatcher are silently ignored.	`{}`

Returns:

Type	Description
`tuple`	`(spc, ops)` from the operator-set builder.

Model Parameters¶

TOML key	Type	Default	Description
`symmetry`	str	`"U1"`	`"U1"` or `"SU2"`
`spin`	float	`0.5`	Site spin quantum number
`J`	float	`1.0`	NN coupling constant
`Jp`	float	`0.0`	NNN coupling constant (requires NNN bonds in geometry)

Hamiltonian¶

\[ H = J \sum_{\langle i,j \rangle} \mathbf{S}_i \cdot \mathbf{S}_j + J' \sum_{\langle\langle i,j \rangle\rangle} \mathbf{S}_i \cdot \mathbf{S}_j \]

For SU(2) symmetry, the full rotational invariance is preserved. For U(1), the spin-z projection is conserved.

build_heisenberg¶