Feature: backport SOC magnetic symmetry and extend LibRPA exports

[bhjia-phys]

Enable the master_ghj RI/LibRPA producer to preserve SOC magnetic-group information, with the upstream conjugate-first spin-density correction. Magnetic exports now include unitary/antiunitary operations and the spin-action trailer; band_out also initializes precision before the first occupation and Fermi energy, avoiding a default-six-digit first row.

Linked upstream work and scope

This targets AroundPeking/abacus-develop:master_ghj at 584c4cfedf92. That branch does not contain the SOC magnetic-group core, so this PR necessarily includes an adapted backport of deepmodeling/abacus-develop#7692, with the original author and source commit retained, the complementary #7513 Pauli-Hamiltonian corrections, and the applicable #7832 spin-density correction. It is not a merge of current upstream develop.

On top of those dependencies:

• Export magnetic operation tables and spin_symmetry metadata for the compatible LibRPA spinor reader.
• Add optional raw active-ABF overlap output and an offline matrix analyzer, with input validation and tests.
• Conjugate scalar-ABF tensors under antiunitary restoration, and retain the production checks rejecting malformed tensor shapes and duplicate restored keys.
• Set all band_out numeric precision before writing the first occupation/Fermi energy.
• Preserve this branch's existing high-angular-momentum Wigner correction, grey-group rotation caching, scalar coefficient/density phase convention and short/long split-Ewald exchange. The SOC caller restores and accumulates each Coulomb channel separately.

Two small pre-existing build defects were isolated against the target and corrected separately: Flag_Finish::Cs must be C for the declared LibRI dependency, and the existing RI I/O test needs the header defining the helper it calls. The comparison baseline includes only these two build fixes.

Core-module behavior

The upstream symmetry implementation handles coupled spin-density components and magnetic operation tables. The density-matrix change corrects extraction of the physical y magnetization from the stored conjugate-first matrix. Solver call sites dispatch the three spin components together. Cell setup forwards the symmetry setting to retain explicitly zero initial moments with symmetry enabled. The corresponding local/Hubbard Pauli-to-spinor conversions, noncollinear force factors and missing ELPA context are backported from deepmodeling#7513; existing target DeltaSpin moment/operator signs are retained.

The RI layer adds the SOC rotation/restoration path while retaining the target's scalar and split-Ewald behavior. The optional overlap export is off by default. See the interface documentation for the file layout, input settings and validation boundaries.

Unit and case tests

Validation uses Intel oneAPI 2024.2, MPI, LibRI v0.2.1.1, LibXC 6.1.0 and matched dependencies on dongfang.

Check	Result
Target baseline release build, with the two build-only fixes above	Pass
Baseline focused CTest targets	7/7 primary targets (30 cases), plus 4/4 cell/API targets (90 cases)
Baseline native SOC reference cases	3/3 cases, 13 properties
Candidate release build and primary CTest targets	13/13 targets, 70 C++ cases
Candidate cell/API targets	4/4 targets, 90 C++ cases
Python ABF analyzer	12/12 tests
Candidate native integration	6/6 cases, 34 compared properties
Native Bi producer-to-LibRPA checks	Pass: both exports, ABF analyzers and EXX reader runs; common-density PBE max difference 3.91694e-9 eV across 2700 star-state pairs
Native FePt producer-to-LibRPA checks	Both exports, ABF analyzers and EXX readers pass on the 1 MPI × 48 thread retry; PBE energy max 1.05950e-9 eV across 5184 star-state pairs; strict occupation postcheck fails as detailed below
SOC split-Ewald operational probe	Pass; both short/long channels active, deliberately loose SCF, no physical convergence claim

Native cases are scf_angle_spin4, scf_out_dos_spin4, scf_u_spin4, scf_out_elf, scf_out_hsr_spin4, and 15_KP_HSE_SOC_symm. The first five use 4 MPI ranks and one thread; so does the HSE case. In the H/S-output case, the inherited comparator checks S and position matrices, energy and symmetry metadata; H-matrix comparison remains disabled in the original driver.

The initial port failed SOC DFT+U by 0.13964911 eV because the density correction was not yet paired with deepmodeling#7513's Hamiltonian fixes. The old producer passed the same input, and the complete backport now passes energy, force and stress. The carbon fixture now includes the full upstream cell and matching H/S/r references (H/S numeric tokens preserved, formatting adapted to the target's CSR format). scf_angle_spin4 carries upstream's original 1e-5 eV threshold file, previously absent from this target. No candidate-generated numerical reference or newly selected tolerance is used.

The last commit changes only the carbon reference fixtures; the executable code is identical to the tested 0bd33e37e build. The five unchanged cases passed together, followed by the carbon case with the complete fixture. Native consumer runs use fresh SOC SCFs, symmetry-on/off exports at a common density, explicit first-occupation checks, spin trailers, active-ABF analysis, and a LibRPA EXX reader smoke test.

Upstream GitHub workflows are currently action_required pending maintainer approval (for example workflow run); the local results above do not establish upstream CI success.

The FePt retry finished in 1 h 51 min 48 s without OOM. Its retained postcheck fails only the normalized occupation criterion: 5.52014e-12 versus 1e-12. The separately solved Fermi levels differ by 2.69651e-12 eV. Recomputing the executed Gaussian occupations explains the observed differences within 3.25e-14; at one common Fermi level the maximum difference becomes 2.06e-13. This is a diagnostic, not altered producer output or a relaxed gate. The unchanged Occupy::efermig electron-count convergence tolerance is 1e-10. The draft retains this strict-gate qualification; no new band-symmetry or reader failure is identified by this check.

Remaining limits

This submission concerns the producer, symmetry components and native consumer interface. It does not claim to repair the separately observed material-dependent reduced-input RPA/GW discrepancies or establish physically converged SOC-GW bands. Native producer-to-consumer checks are additional interface tests; LibRPA's archived-input regression workflow is unchanged. GPU, Python bindings and the complete ABACUS integration suite are outside this focused validation.