[Wannier] Parity-time symmetry
Daniel Kaplan
danielkaplan137 at gmail.com
Tue Dec 31 14:26:36 CET 2019
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
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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
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