Fix: bug of DeltaSpin with nspin=2 for both pw and lcao base

[dyzheng]

Summary

Fixes two independent nspin=2 DeltaSpin (spin-constrained DFT) bugs — one in the
LCAO operator chain and one in the PW occupation output — and refreshes stale
DeltaSpin PW reference values.

The LCAO bug made the spin constraint physically wrong (the constraint acted as a
spin-independent potential), producing incorrect magnetic moments and total
energies. The PW bug corrupted the projected atomic magnetization/occupation
output and the per-atom labels of the DeltaSpin tables.

Branch: fix/deltaspin-lcao-pw-nspin2
Base: deepmodeling/abacus-develop:develop

---

Root cause 1 — LCAO: current_spin was never propagated through the operator chain

HamiltLCAO::updateHk() sets the spin index on the root operator only:

this->getOperatorLCAO()->set_current_spin(this->kv->isk[ik]);

OperatorLCAO::init() did not forward that value to the rest of the chain. Most
operators (Veff, DFT+U, DeePKS) manage their own current_spin by toggling, but
DeltaSpin does not — so for nspin=2 its current_spin was always 0.

DeltaSpin::contributeHR() then does:

coefficients[0] = +delta_lambda_z;   // spin-up
coefficients[1] = -delta_lambda_z;   // spin-down
...
dhr_data[i] += pre_hr_data[i] * coefficients[this->current_spin];

With current_spin == 0 for both channels, +lambda_z was added to both
spin-up and spin-down, i.e. the constraint became a spin-independent potential
that does not split the spins. The lambda loop then optimized against a
Hamiltonian that had no spin response.

Fix

In OperatorLCAO<TK, TR>::init(), propagate current_spin to the next node
before processing the current one:

if (this->next_op != nullptr) {
    dynamic_cast<OperatorLCAO<TK, TR>*>(this->next_op)->current_spin = this->current_spin;
}

Instrumented before/after (first 8 contributeHR calls):

• before: current_spin = 0,0,0,0,...
• after: current_spin = 0,0,1,1,...

Impact (LCAO Fe2, nspin=2, target M = ±2 µB)

case	before	after	accel reference
fixed lambda (loop off)	-6762.4358 eV	-6789.4013179072 eV	-6789.4013179076 eV
lambda loop on	-3001.22 eV, λ diverged to ~1040 eV/µB	-6789.6211 eV, Mtot=0.005, |M|=4.196 µB	-6789.6201 eV, Mtot=0.006, |M|=4.195 µB

After the fix the LCAO result matches the accel branch to ~1e-9 eV and the lambda
loop no longer diverges.

---

Root cause 2 — PW: cal_occupations() mis-read the becp layout for npol=1

OnsiteProjector::cal_occupations() (called when onsite_radius > 0) always used
the npol=2 stride ib*2*nkb and filled all four Pauli blocks, ignoring the spin
channel for nspin=2 (npol=1). The projected atomic magnetization printed by
print_orb_chg() was therefore wrong.

Fix

Index by the psi npol and store the occupancy in the correct Pauli block:

• nspin=2 (npol=1): spin-up → occ[0], spin-down → occ[3], so that
  Charge = occ[0]+occ[3] and Mag(z) = occ[0]-occ[3].
• nspin=1 (npol=1): split evenly between occ[0]/occ[3] so the printed
  magnetization is zero.
• nspin=4 (npol=2): keep the interleaved spinor layout (unchanged).

Additionally:

• print_orb_chg(), print_Mi(), print_Mag_Force() now build per-atom
  labels (Fe1, Fe2, …) instead of passing the per-type label vector
  (size ntype) into tables with nat rows.
• SpinConstrain::get_iat() is made const so the label helpers can read it from
  a const SpinConstrain&.
• cal_occupations() now takes nspin as an explicit argument (passed from
  ctrl_scf_pw(), which already holds the parsed Input_para) rather than
  reading PARAM.inp.nspin, keeping the repository's global-dependency budget
  neutral (required by the governance check).

---

Test reference updates

tests/03_NAO_multik/scf_deltaspin2/result.ref — the previous values encoded the
buggy LCAO result.

tests/17_DS_DFTU/ — five PW cases carried result.ref values written in #7382
that no longer matched the code:

case	old	new
12_PW_DS_S2_Z	-6366.56911826	-6369.19826815
18_PW_DFTU_DS_S2_Z	-6355.98555884	-6360.55555973
19_PW_DFTU_DS_S4_XY	-6360.55545887	-6360.55553395
21_PW_DFTU_DS_S4_Z	-6360.55546554	-6360.55540795
41_PW_DS_S4_Thr10_XY	-6369.19825465	-6369.19825506

12_PW_DS_S2_Z now agrees with the dedicated tests/01_PW/scf_deltaspin2
reference (-6369.19826815 eV), confirming the refreshed value is the intended one.

---

Verification

• LCAO tests/03_NAO_multik/scf_deltaspin2: etot / etotperatom / force / stress pass.
• PW tests/01_PW/scf_deltaspin2: etot / etotperatom / force / stress pass.
• tests/17_DS_DFTU 12, 18, 08, 11, 19, 21, 41: pass.
• Agent Governance checker:
  python3 tools/03_code_analysis/agent_governance_check.py --base <merge-base> --head <head>
  exits 0 (only the non-blocking "Documentation sync review" warning remains).
• Built with the Intel oneAPI toolchain (abacus_basic_para).

---

Files changed

file	change
source/source_lcao/module_operator_lcao/operator_lcao.cpp	propagate current_spin through the operator chain
source/source_lcao/module_deltaspin/spin_constrain.h	make get_iat() const
source/source_lcao/module_deltaspin/lambda_loop_helper.cpp	per-atom labels in print_Mi / print_Mag_Force
source/source_pw/module_pwdft/onsite_proj.h	cal_occupations() takes nspin
source/source_pw/module_pwdft/onsite_proj_overlap.cpp	fix npol=1 becp indexing / Pauli blocks
source/source_pw/module_pwdft/onsite_proj_print.cpp	per-atom labels in print_orb_chg
source/source_io/module_ctrl/ctrl_output_pw.cpp	pass inp.nspin to cal_occupations
tests/03_NAO_multik/scf_deltaspin2/result.ref	refresh LCAO reference
tests/17_DS_DFTU/{12,18,19,21,41}_*/result.ref	refresh stale PW references

---

Notes

• The LCAO fix is the develop-side counterpart of accel's 8c838a293; the PW fix
  corresponds to accel's 8801a66ee.
• The five 17_DS_DFTU PW references are intentionally refreshed in this PR; they
  are test-data-only changes.