Abnormal energies in z direction for an isotropic magnetic system in non collinear calculation with soc

[hongriTianqi]

Describe the bug

The system is BCC Fe. I performed NC+SOC calculation with starting mag moments in x, y, and z directions. The results come as:

ground_stateX/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.996537401447 eV
ground_stateY/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.996537402879 eV
ground_stateZ/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.996142674576 eV

the magnetimc moment results:

ground_stateX/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (3.62, 0, 0)
ground_stateX/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (3.62, 0, 0)
ground_stateY/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 3.62, 0)
ground_stateY/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 3.62, 0)
ground_stateZ/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 0, 3.621)
ground_stateZ/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 0, 3.621)

Expected behavior

The results on different directions are assumed to be exactly the same for this isotropic magnetic system.

To Reproduce

issue_soc.tar.gz

Environment

No response

Additional Context

No response

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[hongriTianqi]

details of energy terms

[hongriTianqi]

By using exactly the same inputs, but set lspinorb false, the results are isotropic:

ground_stateX/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.853714332487 eV
ground_stateY/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.853714333552 eV
ground_stateZ/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.853714333698 eV

Mag results:

ground_stateX/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (3.625, 0, 0)
ground_stateX/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (3.625, 0, 0)
ground_stateY/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 3.625, 0)
ground_stateY/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 3.625, 0)
ground_stateZ/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 0, 3.625)
ground_stateZ/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 0, 3.625)

[hongriTianqi]

results.zip

[hongriTianqi]

I think this issue is related to #2290.

[hongriTianqi]

This will be fixed by a pr, the results becomes:

ground_stateX/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.996537401447 eV
ground_stateY/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.996537402879 eV
ground_stateZ/OUT.ABACUS/running_scf.log: !FINAL_ETOT_IS -6817.996537402360 eV

The cause of this issue is inside source/module_elecstate/module_charge/charge_mixing.cpp

  for (int is = 0; is < GlobalV::NSPIN; ++is)
    {
        if (is == 0 || is == 3 || !GlobalV::DOMAG_Z)
        {
            double* rho123_is = rho123.data() + is * nrxx;
#ifdef _OPENMP
#pragma omp parallel for schedule(static, 512)
#endif
            for(int ir = 0 ; ir < nrxx ; ++ir)
            {
                chr->rho_save[is][ir] = rho123_is[ir];
            }
        }
    }

for x, y directions, GlobalV::DOMAG_Z is false, but for z direction GlobalV::DOMAG_Z is true, which results in inconsistency of rho_save between z and xy directions. Then the E_descf is different between scf steps.

[hongriTianqi]

The magnetic moments also become exactly the same in NC + SOC computation:

ground_stateX/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (3.62, 0, 0)
ground_stateX/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (3.62, 0, 0)
ground_stateY/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 3.62, 0)
ground_stateY/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 3.62, 0)
ground_stateZ/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 0, 3.62)
ground_stateZ/OUT.ABACUS/mulliken.txt:Total Magnetism on atom:  Fe                   (0, 0, 3.62)

[hongriTianqi]

This issue designs simple benchmark test cases to debug, so is good practice.