Hello All! I was wondering if any of you have encountered the following issue when fitting wannier functions in systems with specific symmetry.
I'm dealing with a magnetic system (but in principle, this could be any system) which has PT-symmetry. Since [PT, H] = 0, but in general, PT does not commute with other observables, the spectrum of H should be of doubly-degenerate bands (much like Kramers' degeneracy). Indeed a self-consistent VASP run converges to such a spectrum remarkably well, with the splitting between bands less than 1meV. The trouble begins when attempting to fit Wannier functions to this system. While overall the fit is of good quality (see attached spread information; and band-structure comparisons) in many places along the high-symmetry lines the splitting between bands amounts to >10meV which is unacceptable in terms of preserving the symmetry. More to the point the Wannier90.eig file *DOES *carry the symmetry rather well (most eigenvalues differ by less than 1meV), but then throughout the band-structure this is no longer the case. What would you recommend in this instance? I was thinking as well about the possibility of imposing this symmetry directly. Since any Bloch band \phi(k) has a PT-partner PT \phi(k), and these are naturally degenerate, then it would make a lot of sense (at least, superficially) to fit the Wannier bands to *half* the spectrum, and then reconstruct the other half by applying PT on the eigenvectors composed of the Wannier basis. Is such a thing at all possible? Yours thankful, Daniel Kaplan Dept. of Condensed Matter Physics Weizmann Institute of Science
Final State WF centre and spread 1 ( 0.804077, 0.102310, 7.704753 ) 6.13299382 WF centre and spread 2 ( 0.082185, -0.995229, 8.438850 ) 5.82641191 WF centre and spread 3 ( -0.556984, -0.688866, 7.673939 ) 5.45609639 WF centre and spread 4 ( 0.004711, -0.006884, 6.174897 ) 1.48160342 WF centre and spread 5 ( -0.003941, 0.036428, 6.218878 ) 2.24103642 WF centre and spread 6 ( 0.000440, 0.020881, 6.222547 ) 1.74400990 WF centre and spread 7 ( 0.002633, -0.001175, 6.077481 ) 1.48137326 WF centre and spread 8 ( -0.013331, -0.078053, 6.020684 ) 4.81346904 WF centre and spread 9 ( -0.047670, -0.613716, 1.634524 ) 5.38254812 WF centre and spread 10 ( 0.996041, -0.924214, 3.327170 ) 5.39097450 WF centre and spread 11 ( -0.032994, 1.252665, 4.029649 ) 5.79797902 WF centre and spread 12 ( -0.005517, 0.006678, 3.102633 ) 1.49462375 WF centre and spread 13 ( 0.000154, -0.010012, 3.063406 ) 1.52701405 WF centre and spread 14 ( -0.001518, -0.009227, 3.055703 ) 1.99828982 WF centre and spread 15 ( -0.000300, -0.005523, 3.163580 ) 1.23192042 WF centre and spread 16 ( 0.015073, 0.076194, 3.251327 ) 4.80945433 WF centre and spread 17 ( 0.030989, 0.237591, 0.590173 ) 6.60630368 WF centre and spread 18 ( -1.772519, 0.312462, 0.139756 ) 6.46630010 WF centre and spread 19 ( 0.597293, 0.651979, -0.300591 ) 6.03041340 WF centre and spread 20 ( -0.587732, 0.663604, -0.288734 ) 5.96616358 WF centre and spread 21 ( 0.738419, -0.075074, 1.552730 ) 5.79103262 WF centre and spread 22 ( 0.564951, -0.693327, 0.279969 ) 6.06113163 WF centre and spread 23 ( 0.548477, -0.635296, -1.603221 ) 5.45568554 WF centre and spread 24 ( -0.265593, -1.678647, -0.018321 ) 6.58644738 WF centre and spread 25 ( 0.046136, 0.629771, 7.651816 ) 5.55234929 WF centre and spread 26 ( -1.003588, 0.899042, 5.894349 ) 5.36205748 WF centre and spread 27 ( 0.053748, -1.223677, 5.304028 ) 5.65578315 WF centre and spread 28 ( 0.005018, -0.006578, 6.173327 ) 1.49567169 WF centre and spread 29 ( 0.000792, 0.009804, 6.211000 ) 1.52611206 WF centre and spread 30 ( 0.001658, 0.008597, 6.221223 ) 1.99849887 WF centre and spread 31 ( 0.000367, 0.006770, 6.109200 ) 1.25106501 WF centre and spread 32 ( 0.001845, 0.006039, 6.173635 ) 0.85020681 WF centre and spread 33 ( -0.780292, -0.083807, 1.577272 ) 6.31874999 WF centre and spread 34 ( 0.558295, 0.665169, 1.609991 ) 5.51721942 WF centre and spread 35 ( -0.502955, 0.668043, 1.618807 ) 5.41476590 WF centre and spread 36 ( -0.005656, 0.006442, 3.100879 ) 1.48123683 WF centre and spread 37 ( 0.003781, -0.036888, 3.056105 ) 2.23419551 WF centre and spread 38 ( -0.000504, -0.020705, 3.054638 ) 1.73936367 WF centre and spread 39 ( -0.004864, 0.001035, 3.199091 ) 1.49755288 WF centre and spread 40 ( -0.001232, -0.004520, 3.102499 ) 0.86077465 WF centre and spread 41 ( -0.030562, -0.217701, -0.618899 ) 6.59640398 WF centre and spread 42 ( 1.755124, -0.337636, -0.142115 ) 6.44678022 WF centre and spread 43 ( -0.599205, -0.652313, 0.301883 ) 6.00746636 WF centre and spread 44 ( -0.707285, -0.821000, 1.266723 ) 5.32716531 WF centre and spread 45 ( -0.715087, 0.039541, -1.558092 ) 5.82060536 WF centre and spread 46 ( 0.702607, 0.838813, -1.214371 ) 5.34751441 WF centre and spread 47 ( -0.082374, 1.036800, 0.771103 ) 5.88128621 WF centre and spread 48 ( 0.228054, 1.669972, 0.020484 ) 6.64394103 Sum of centres and spreads ( 0.021167, 0.026564,148.396357 ) 202.60004219 Spreads (Ang^2) Omega I = 130.040382817 ================ Omega D = 1.666441675 Omega OD = 70.893217703 Final Spread (Ang^2) Omega Total = 202.600042195
wannier90.win
Description: Binary data
wannier90.eig
Description: Binary data
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