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build_conductor

Load spinful-fermion (Band) space and build MPO operator templates.

build_conductor 

build_conductor(symmetry: str = 'U1,SU2') -> Tuple[Index, Dict[str, Tensor]]

Load spinful-fermion (Band) space and build MPO operator templates.

Calls load_space('Band', symmetry) and enriches the returned Op dictionary with derived operators for use in MPO construction of spinful tight-binding and Hubbard-type models.

Parameters:

Name Type Description Default
symmetry str

Band symmetry string — 'U1,U1', 'Z2,U1', 'U1,SU2' (default), or 'Z2,SU2'.

 'U1,SU2'

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 what load_space returns):

Hopping-type (2-site) operators — Jordan-Wigner dressed:

  • 'F' (Abelian only) — combined annihilator F_up + F_dn; overwrites the key for uniformity with the SU2 case.
  • 'ZF' — JW-dressed annihilator Z × F for the leading site.
  • 'ZC' — JW creator (ZF)† with op_OUT (adjusted via capcup); leading-site creation channel.
  • 'Fd' — bare creator F† with op_IN; terminal-site creation channel.
  • 'Cd' — bare annihilator copy with op_IN (adjusted via capcup); terminal-site annihilation channel.
  • 'G' — oplus(ZF, ZC, axes=2), JW combined leading-site op.
  • 'Gdag' — oplus(Fd, Cd, axes=2), bare terminal-site op.
  • 'G4', 'G4dag' — 4th-order leading- and terminal-site templates.

Spin operators:

  • 'S' — 3rd-order spin operator; for SU2 taken directly from Op['S']; for Abelian built as Sp + Sm + Sz (with op axis inserted on Sz, which load_space returns without one).
  • 'Sdag', 'S4', 'S4dag' — adjoint and 4th-order templates.
  • 'Sp4', 'Sp4dag', 'Sm4', 'Sm4dag' (Abelian only) — same layouts as S4/S4dag but for Sp and Sm individually.
  • 'Sz4', 'Sz4dag' (Abelian only) — templates for Sz alone.

On-site operators:

  • 'N' — 2nd-order total number operator n_up + n_dn.
  • 'NN' — 2nd-order double-occupancy operator n_up × n_dn.
  • 'N4', 'NN4', 'I4', 'Z4' — 4th-order on-site tensors.
  • 'Z4mid' — 4th-order intermediate-site template for long-range Hubbard hopping bonds (op_IN, op_OUT, bra_OUT, ket_IN); applies Z at each intermediate site for the Jordan-Wigner string.

See Also