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<div class="WordSection1">
<p class="MsoNormal">Dear QE community,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I am investigating a system with noncollinear spin and +U correction, but without starting_magnetization. Due to the following sentence in the pw.x input description, I would expect this calculation to exhibit time-reversal symmetry:<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal" style="margin-left:.5in">In the spin-orbit case starting with zero starting_magnetization on all atoms imposes time reversal symmetry. The magnetization is never calculated and kept zero (the internal variable domag is .FALSE.).<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">However, the states at k=Gamma are <i>not</i> Kramers pairs (doubly degenerate), indicating that time-reversal symmetry is broken.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">To illustrate the behavior on a simplified example, I have modified the Fe calculation from the test suite as follows [1]:
<o:p></o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l3 level1 lfo3">Remove the starting_magnetization and related inputs<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l3 level1 lfo3">Create a 2x2x2 supercell and randomly displace the atoms to break all spatial symmetries (using ASE’s rattle method with stddev=0.01 Angstrom) [2]<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l3 level1 lfo3">Reduce the hubbard_U and hubbard_J by a factor of 2, to (presumably?) tune the system out of the ferromagnetic regime [3]<o:p></o:p></li></ul>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The resulting input files can be found in the attachments, or pasted below. With +U correction [with_u.in], the energies at Gamma [4] are split by ~0.06meV on average, and up to ~0.46 meV. Without +U [without_u.in], the average split is
~3.6e-08 meV, and the maximum is ~3.6e-07 meV.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I would appreciate any input on the following questions:<o:p></o:p></p>
<ul style="margin-top:0in" type="disc">
<li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo6">Does QE take time-reversal symmetry into account explicitly (by symmetrizing the relevant quantities), or implicitly (by selection of symmetry-inequivalent k-points)?<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo6">If the latter, is there any way to explicitly enforce time-reversal symmetry?<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo6">Is there anything about +U correction in particular that could break time-reversal symmetry (on a technical level, not because it tends to produce magnetic states)?<o:p></o:p></li><li class="MsoListParagraph" style="margin-left:0in;mso-list:l0 level1 lfo6">Or is there anything about this combination of attributes that means this calculation doesn’t make sense?<o:p></o:p></li></ul>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Thank you and best regards,<o:p></o:p></p>
<p class="MsoNormal">Dominik<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">---<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-size:10.0pt;color:#7F7F7F">Dr. Dominik Gresch<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;color:#7F7F7F"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;color:#7F7F7F">Simulation Engineer<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="DE-CH" style="font-size:10.0pt;color:#7F7F7F">Microsoft Quantum<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">[1] This isn’t expected to be a <i>physically</i> correct calculation.<o:p></o:p></p>
<p class="MsoNormal" style="background:white"><span style="color:black">[2] This is to get rid of any degeneracies enforced by symmetries other than time-reversal.<br>
[3] Without this change the calculation didn’t converge without starting_magnetization. This wasn’t a problem for the system I am trying to study (which I unfortunately cannot share), but maybe it is somehow related to the reason why time-reversal is broken?<br>
[4] Taking into account only occupied states, since the unoccupied ones are converged to lower accuracy.<br>
<br>
<b>Version details:</b> PWSCF v6.6, compiled with GCC v9.2.0, FFTW v3.3.8, MVAPICH2 v2.3.4, Netlib-SCALAPACK v2.1.0, OPENBLAS v0.3.10, run on Zen2 architecture</span><span style="font-size:10.0pt;font-family:Consolas"><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><b>[with_u.in]<o:p></o:p></b></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">&CONTROL<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> calculation = 'scf'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> disk_io = 'low'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> outdir = './out/'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> prefix = 'aiida'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> pseudo_dir = './pseudo/'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> verbosity = 'low'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">/<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">&SYSTEM<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> degauss = 1.0000000000d-02<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> ecutrho = 280<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> ecutwfc = 35<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> hubbard_j(1,1) = 8.7500000000d-01<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> hubbard_j(2,1) = 0.0000000000d+00<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> hubbard_u(1) = 1.1000000000d+00<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> ibrav = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> lda_plus_u = .true.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> lda_plus_u_kind = 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> lspinorb = .true.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> nat = 8<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> nbnd = 142<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> noncolin = .true.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> ntyp = 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> occupations = 'smearing'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> smearing = 'mv'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">/<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">&ELECTRONS<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> conv_thr = 1.0000000000d-08<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">/<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">ATOMIC_SPECIES<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 55.845 Fe.rel-pbe-spn-rrkjus_psl.0.2.1.UPF<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">ATOMIC_POSITIONS angstrom<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 0.0049671415 -0.0013826430 0.0064768854
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 1.4502302986 1.4326584663 -1.4373413696
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 1.4507921282 -1.4273256527 1.4303052561
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 2.8754256004 -0.0046341769 -0.0046572975
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe -1.4325803773 1.4158671976 1.4177508217
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe -0.0056228753 2.8598716888 0.0031424733
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe -0.0090802408 -0.0141230370 2.8846564877
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 1.4327422370 1.4356752820 1.4207525181
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">K_POINTS automatic<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">4 4 4 0 0 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">CELL_PARAMETERS angstrom<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> -2.8700000000 2.8700000000 2.8700000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> 2.8700000000 -2.8700000000 2.8700000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> 2.8700000000 2.8700000000 -2.8700000000<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><b>[without_u.in]<o:p></o:p></b></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">&CONTROL<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> calculation = 'scf'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> disk_io = 'low'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> outdir = './out/'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> prefix = 'aiida'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> pseudo_dir = './pseudo/'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> verbosity = 'low'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">/<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">&SYSTEM<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> degauss = 1.0000000000d-02<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> ecutrho = 280<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> ecutwfc = 35<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> ibrav = 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> lspinorb = .true.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> nat = 8<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> nbnd = 142<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> noncolin = .true.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> ntyp = 1<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> occupations = 'smearing'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> smearing = 'mv'<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">/<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">&ELECTRONS<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> conv_thr = 1.0000000000d-08<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">/<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">ATOMIC_SPECIES<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 55.845 Fe.rel-pbe-spn-rrkjus_psl.0.2.1.UPF<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">ATOMIC_POSITIONS angstrom<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 0.0049671415 -0.0013826430 0.0064768854
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 1.4502302986 1.4326584663 -1.4373413696
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 1.4507921282 -1.4273256527 1.4303052561
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 2.8754256004 -0.0046341769 -0.0046572975
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe -1.4325803773 1.4158671976 1.4177508217
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe -0.0056228753 2.8598716888 0.0031424733
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe -0.0090802408 -0.0141230370 2.8846564877
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">Fe 1.4327422370 1.4356752820 1.4207525181
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">K_POINTS automatic<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">4 4 4 0 0 0<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas">CELL_PARAMETERS angstrom<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> -2.8700000000 2.8700000000 2.8700000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> 2.8700000000 -2.8700000000 2.8700000000<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.0pt;font-family:Consolas"> 2.8700000000 2.8700000000 -2.8700000000<o:p></o:p></span></p>
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