[WIP] Implicit derivatives for CTMRG

[leburgel]

Adds implicit gradients for CTMRG contractions.

Reference: https://arxiv.org/abs/2607.15030

[codecov]

Codecov Report

❌ Patch coverage is 89.56743% with 41 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
...hms/contractions/ctmrg/characteristic_equations.jl	87.13%	35 Missing ⚠️
...lgorithms/optimization/implicit_differentiation.jl	94.91%	6 Missing ⚠️

Files with missing lines	Coverage Δ
src/Defaults.jl	85.71% <ø> (ø)
src/algorithms/ctmrg/c4v.jl	83.48% <100.00%> (-0.45%)	⬇️
src/algorithms/ctmrg/sequential.jl	98.43% <100.00%> (+0.02%)	⬆️
src/algorithms/optimization/peps_optimization.jl	94.73% <ø> (ø)
...lgorithms/optimization/implicit_differentiation.jl	91.77% <94.91%> (ø)
...hms/contractions/ctmrg/characteristic_equations.jl	87.13% <87.13%> (ø)

... and 2 files with indirect coverage changes

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[github-actions]

After the build completes, the updated documentation will be available here

[pbrehmer]

Looks really good to me! I would personally like to give SequentialCTMRG with implicit differentiation a try but we can of course also postpone this to a later PR.

[leburgel]

Windows CI is completely refusing to work for some reason, but other than that I think this has pretty much everything I had in mind for now.

[pbrehmer]

Looks good to merge to me now! The Windows CI problems look like they are not really related to this PR in particular and rather some CI setup issue, if I'm not mistaken.