Symmetrization M0: add characterization harness, capture multi-band bug

[tylersax]

Add a per-(model, point-group) characterization harness for single-particle cluster symmetrization, generalizing the existing identity-only symmetrize_test onto real point groups. It is the regression net for upcoming Hamiltonian- derived symmetrization work.

Oracle: G0 = [iw + mu - H0]^-1 is deterministic and exactly invariant under every symmetry of H0, so symmetrizing G0 must be a no-op (asserted to 1e-12).

Note: this harness flagged a failure, and it captures that failure on purpose. Production Symmetrize::execute is not a no-op on the three-band Hubbard model with D4 symmetry. Given the exact, deterministic oracle, the failure is treated as an existing defect in the imposition. Rather than commit a red test, the observed failures are encoded as the expected result. So, read this test fixture as both the record of the bug and the gate for its fix: when the imposition is corrected, the assertion flips (forcing the test to be cleaned up).

Structure: Four tests per case, one binary per case selected via CMake TEST_DEFINES.

Building & running

cmake -S . -B build -DDCA_WITH_TESTS_FAST=ON

cmake --build build -j --target \
  symmetrize_characterization_square_D4_test \
  symmetrize_characterization_threeband_D4_test \
  symmetrize_characterization_singleband_chain_test

ctest --test-dir build -R symmetrize_characterization --output-on-failure

Expected result

All three binaries PASS, including the three-band case.

The threeband_D4 binary prints per-representation diagnostics that include lines like:

  k_iw: FAIL  max|G0 - sym(G0)| = 0.27...

These FAIL lines are the captured-baseline residuals.

[PDoakORNL]

I think this is actually a nice example of an integration test so I'd move it to test/integration/phys/symmetrization
Which will be a new category of integration test for us.
So the only thing I see right now is move this.

Generally I'd say for unit tests you need a class or function(in which case I'd treat the filename as the class for purposes of naming the test) that you are trying to test as standalone as possible (within reason).

[tylersax]

Good call, this makes a lot more sense as integration. Updated (with local re-test passing).

[PDoakORNL]

This LGTM now.