Correlator for purified iPEPO and right-to-left contraction

[Yue-Zhengyuan]

This PR improves the correlator function by adding support for purified iPEPO and removing some constraints on sites js, with some under-the-hood deduplications.

• Deduplicate iPEPS and one-layer iPEPO trace correlator logic through private correlator context/adapters.
• Add purified iPEPO correlators:

  correlator(bra::InfinitePEPO, O, i, js, ket::InfinitePEPO, env::CTMRGEnv)

  matching the purified-state convention used by expectation_value.
• Generalize horizontal correlators so js may contain targets on either side of i.
  • js no longer need to be sorted.
  • js can contain sites on both sides of i.
  • Output order follows vec(js).
  • j == i is rejected with ArgumentError.
• Vertical correlators inherit the same behavior through dispatching to horizontal correlators via rotation.
• Add right-to-left correlator contractions and the corresponding edge_transfer_right paths for js on the left of i.

Implementation Notes

The shared correlator implementation now dispatches through private context types:

• _PEPSCorrelator
• _PEPOPurifiedCorrelator
• _PEPOTraceCorrelator

The horizontal sweep partitions js into right and left sites internally:

• right targets use the existing left-to-right contraction path;
• left targets use a mirrored right-to-left contraction path;
• results are written back into the original target order.

Low-level tensor contractions remain separate where the tensor ranks genuinely differ.

[codecov]

Codecov Report

❌ Patch coverage is 92.69231% with 19 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/algorithms/correlator_adapters.jl	84.61%	18 Missing ⚠️
src/algorithms/transfermatrix.jl	90.00%	1 Missing ⚠️

Files with missing lines	Coverage Δ
.../algorithms/contractions/correlator/pepo_1layer.jl	100.00% <100.00%> (ø)
...lgorithms/contractions/correlator/pepo_purified.jl	100.00% <100.00%> (ø)
src/algorithms/contractions/correlator/peps.jl	100.00% <100.00%> (ø)
src/algorithms/contractions/transfer.jl	91.66% <100.00%> (+22.91%)	⬆️
src/algorithms/correlators.jl	100.00% <100.00%> (+3.12%)	⬆️
src/algorithms/toolbox.jl	96.92% <ø> (ø)
src/networks/local_sandwich.jl	85.71% <100.00%> (+0.52%)	⬆️
src/algorithms/transfermatrix.jl	80.00% <90.00%> (+13.33%)	⬆️
src/algorithms/correlator_adapters.jl	84.61% <84.61%> (ø)

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[Yue-Zhengyuan]

Since the V tensors (partially contracted correlator network) are not actually CTMRG edge tensors, I prefer just annotate their type using AbstractTensorMap.

[Yue-Zhengyuan]

A recent idea: in almost all applications, the two-site operator passed to correlator is made from two one-site operators, so the MPO has virtual dimension 1 (although it carries a non-trivial charge in general). Then can we first calculate the product of the MPO and the ket state (or the iPEPO), fusing the MPO virtual leg into the state? In this way, we can get rid of the edge_transfer functions carrying the "excited" leg from the MPO. The computational cost should remain almost the same.