Non-Hermitian and non-covariant H(R) output in ABACUS v3.11.0-beta10 #8121

Describe the bug

In a converged noncollinear LCAO calculation without SOC, the exported hrs1_nao.csr does not satisfy Hermiticity or the expected spin-covariance relation. Symmetry/convention checks indicate that the problem lies in the imaginary part, while the real part agrees with the reference within numerical precision. The maximum residual of H(R) - H(-R)^dagger is 0.0248658696 Ry, and bands reconstructed from the exported Hamiltonian disagree with the SCF energy log. Please check the imaginary-part sign/conjugation convention in the H(R) output.

Relevant INPUT parameters:

calculation scf
basis_type lcao
ks_solver genelpa
dft_functional lda
nspin 4
noncolin 1
lspinorb 0
symmetry -1
ecutwfc 120
kspacing 0.1 0.1 1
scf_nmax 100
scf_thr 1e-6
sc_mag_switch 0
out_mat_hs2 1

Expected behavior

abacus_beta10_example.zip

To Reproduce

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Environment

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Additional Context

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