Use the full corner inverse in C4v characteristic equations for C4vQRProjector

[leburgel]

The C4v characteristic equation for the projector parametrization u contains the inverse of the fixed-point corner. generate_symmetric_characteristic_equation computed it as sdiag_pow(real(DiagonalTensorMap(Cfp)), -1), which inverts only the diagonal of Cfp. That is exact for C4vEighProjector, whose fixed-point corner is the diagonal matrix of eigenvalues, but not for C4vQRProjector: its corner is the Hermitian part of the contracted edges, which is not diagonal. ImplicitGradient with C4vQRProjector therefore solved the wrong linear problem and returned a slightly wrong gradient.

This PR selects the inverse by projector algorithm, through a new internal _c4v_corner_inverse(projector_alg, C):

• C4vEighProjector: unchanged, the inverse of the diagonal.
• C4vQRProjector: the full inverse, computed as V * sdiag_pow(D, -1) * V' from eigh_full(C). This uses the same sdiag_pow as the diagonal case, including its cutoff on small eigenvalues.

generate_symmetric_characteristic_equation takes the projector algorithm as a new projector_alg keyword, which the ImplicitGradient rrule passes.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

Files with missing lines	Coverage Δ
...hms/contractions/ctmrg/characteristic_equations.jl	93.14% <100.00%> (+93.14%)	⬆️
src/algorithms/ctmrg/projectors/c4v_eigh.jl	76.47% <100.00%> (+76.47%)	⬆️
src/algorithms/ctmrg/projectors/c4v_qr.jl	64.28% <100.00%> (+64.28%)	⬆️
...lgorithms/optimization/implicit_differentiation.jl	90.71% <100.00%> (+90.71%)	⬆️

... and 94 files with indirect coverage changes

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[pbrehmer]

Great catch! I have nothing to add, so this looks good to me. (CTMRG failures are unrelated, so this should be ready to be merged.)