Support fermionic sites in simple update and belief propagation#6
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The simple-update gauge reads each environment's ket and bra legs from the state tensor and takes the Hermitian square root in the transposed bipartition, which carries the fermionic braid sign on the odd-parity sector. Doubled ket/bra messages normalize by their trace rather than an entrywise sum, which is sign-correct on fermionic bonds. Operator construction routes through project_aux, so a parity-odd operator gets an auxiliary charge leg instead of throwing, and project_pair builds operator pairs that share a contractible aux leg for fermion strings like c†c.
Rename local index variables (ket_ind/bra_ind, codomain_inds/domain_inds, projected_a), factor an is_operator predicate out of the belief-propagation message normalization instead of inlining the primed-index check, and tighten comments.
The fermionic simple-update and belief-propagation path relies on the corrected fermionic operator contraction from GradedArrays 0.14, which requires TensorAlgebra 0.17.6. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Summary
Makes the belief-propagation simple-update path sign-correct on parity-graded (fermionic) sites, and adds the operator-construction support fermionic sites need.
The simple-update gauge reads each environment's ket and bra legs from the state tensor and takes the Hermitian square root in the transposed bipartition, which carries the fermionic braid sign on the odd-parity sector. Doubled ket/bra messages normalize by their trace rather than an entrywise sum, which is sign-correct on fermionic bonds. Operator construction routes through
project_aux, so a parity-odd operator (X/Y, barec/c†) gets an auxiliary charge leg instead of throwing, andproject_pairbuilds operator pairs that share a contractible auxiliary leg for fermion strings likec†c.Builds on the ITensorBase backend work in JoeyT1994#78, which it targets as its base.