build_fermionic¶

Load spinless-fermion space and build MPO operator templates.

build_fermionic ¶

build_fermionic(symmetry: str = 'U1') -> Tuple[Index, Dict[str, Tensor]]

Load spinless-fermion space and build MPO operator templates.

Calls load_space('Ferm', symmetry) and enriches the returned Op dictionary with derived operators for use in MPO construction.

Parameters:

Name	Type	Description	Default
`symmetry`	`str`	Symmetry string — `'U1'` (conserve particle number) or `'Z2'` (fermion parity).	`'U1'`

Returns:

Type	Description
`tuple`	`(Spc, Op)` where `Spc` is the physical `Index` and `Op` is the enriched operator dictionary.

Notes

New entries added to Op (beyond the 'F', 'Z', 'vac' returned by load_space):

Hopping-type (2-site) operators:

'C' — creator with op_OUT; built from F† and adjusted via capcup so its op direction matches F for use in oplus.
'Fd' — adjoint annihilator (= F†) with op_IN; used as the creator channel in the terminal-site operator.
'Cd' — adjoint creator with op_IN; built from C† and adjusted via capcup.
'G' — oplus(F, C, axes=2), combined 3^rd-order leading-site operator (annihilation and creation channels share the op axis).
'Gdag' — oplus(Fd, Cd, axes=2), combined 3^rd-order terminal-site operator.
'G4', 'G4dag' — 4^th-order leading- and terminal-site templates.

On-site operators:

'N' — 2^nd-order number operator c†c in (bra, ket) layout.
'N4', 'I4', 'Z4' — 4^th-order on-site tensors with trivial L/R bonds.
'Z4mid' — 4^th-order intermediate-site template for long-range fermionic bonds (op_IN, op_OUT, bra_OUT, ket_IN); applies Z (Jordan-Wigner string) at each intermediate site to maintain the correct fermionic sign.