-
Notifications
You must be signed in to change notification settings - Fork 0
/
assembleMeanFieldHamiltonian_gpu.m
513 lines (452 loc) · 17 KB
/
assembleMeanFieldHamiltonian_gpu.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
function [H_alpha,H_beta] = assembleMeanFieldHamiltonian_gpu(state_multiplicity,tensors,SpinOp,Qtensors,SpinXiXjOp,...
theory,zeroIndex,methyl_number, MeanFieldCoefficients, MeanFieldTotal)
% Extract boolean flags.
useEZ = theory(1);
useNZ = theory(2);
useHF_SzIz = theory(3);
useHF_SzIxy = theory(4);
useNucA = theory(5);
useNucB = theory(6);
useNucCD = theory(7);
useNucEF = theory(8);
useNQ = theory(9);
useMeanField= theory(10);
clusterSize = numel(state_multiplicity);
% Adjust for methyl groups.
%Cluster = sort(unique(Cluster));
%if methyl_number==0 && abs(double(zeroIndex) + 1 - double(Cluster(1)) )>=1
% error('Cluster reference failure.');
%end
%if clusterSize ~= length(Cluster)
% error('Cluster reference failure.');
%end
I0 = SpinOp(:,:,1);
Hnuc = 0;
Hhf = 0;
% ENUM
E = 1; Z = 2; RAISE = 3; SZ = 4;
Hmf = 0;
Hmf0 = 0;
Hmf0_ = 0;
% iSpin is the index of the nuclear spin in the cluster
for iSpin = 1:clusterSize
% the ith nuclear spin in the input Hamiltonian
% inucleus = ispin - zeroIndex + 1; % since the electron is given position 1
%------------------------------------------------------------------------
% One Nucleus Spin Hamiltonian
%------------------------------------------------------------------------
% Calculate nuclear Zeeman Hamiltonian
[z,p,m] = spinopidx(clusterSize,iSpin);
Iz = SpinOp(:,:,z);
Ix = (SpinOp(:,:,p) + SpinOp(:,:,m) )/2;
Iy = (SpinOp(:,:,p) - SpinOp(:,:,m) )/2i;
if useMeanField
Hmf0 = Hmf0 - MeanFieldCoefficients(iSpin,iSpin,E)*I0;
Hmf0 = Hmf0 - MeanFieldCoefficients(iSpin,iSpin,Z)*Iz;
Hmf0 = Hmf0 - MeanFieldCoefficients(iSpin,iSpin,RAISE)*SpinOp(:,:,p);
Hmf0 = Hmf0 - MeanFieldCoefficients(iSpin,iSpin,RAISE)'*SpinOp(:,:,m);
Hmf = Hmf - MeanFieldCoefficients(iSpin,iSpin,SZ)*I0;
end
%------------------------------------------------------------------------
% Loop over all nuclei with index greater than the ith nucleus.
%------------------------------------------------------------------------
for jSpin = iSpin+1:clusterSize
% the jth nuclear spin in the input Hamiltonian
%jnucleus = jspin - zeroIndex + 1; % since the electron is given position 1
% get dipolar coupling tensor
dd = tensors(:,:,iSpin+1,jSpin+1) + tensors(:,:,jSpin+1,iSpin+1);
[zz,rl,lr,zr,zl,rz,lz,rr,ll] = spinopidx2(clusterSize,iSpin,jSpin);
if useMeanField
Hmf0_ = MeanFieldCoefficients(jSpin,iSpin,Z)*Iz;
Hmf0_ = Hmf0_ - MeanFieldCoefficients(jSpin,iSpin,RAISE)*SpinOp(:,:,p);
Hmf0_ = Hmf0_ - MeanFieldCoefficients(jSpin,iSpin,RAISE)'*SpinOp(:,:,m);
[z_,p_,m_] = spinopidx(clusterSize,jSpin);
Hmf0_ = Hmf0_ - MeanFieldCoefficients(iSpin,jSpin,Z)*SpinOp(:,:,z_);
Hmf0_ = Hmf0_ - MeanFieldCoefficients(iSpin,jSpin,RAISE)*SpinOp(:,:,p_);
Hmf0_ = Hmf0_ - MeanFieldCoefficients(iSpin,jSpin,RAISE)'*SpinOp(:,:,m_);
end
Hmf0 = Hmf0 + Hmf0_;
end
end
% Calculate total nuclear Hamiltonians for alpha and beta electron manifolds
H_alpha = +1/2*Hmf + Hmf0;
H_beta = -1/2*Hmf + Hmf0;
% Check Hermitianity
threshold = 1e-12;
[isHermA,nonHermiticityA] = isHermitian(H_alpha,threshold);
[isHermB,nonHermiticityB] = isHermitian(H_beta,threshold);
if ~isHermA || ~isHermB
hline = '--------------------------------------------------------------';
disp('!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!');
fprintf('Non-Hermiticity = {%d,%d}.\n',nonHermiticityA,nonHermiticityB);
disp(hline);
disp('!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!');
error('Cluster Hamiltonian is not Hermitian.');
end
% Hermitianize
H_alpha = (H_alpha+H_alpha')/2;
H_beta = (H_beta+H_beta')/2;
end
%{
--------------------------------------------------------------------------
ENUM 1-Clusters: E O
--------------------------------------------------------------------------
E (1) : E
O (2-4): z + -
--------------------------------------------------------------------------
2-Clusters: EE EO OE OO
--------------------------------------------------------------------------
EE (1) : EE
EO (2-4) : Ez E+ E-
OE (5-7) : zE +E -E
OO (8-10): zz +- -+
--------------------------------------------------------------------------
ENUM 3-Clusters: EEE EEO EOE OEE EOO OEO OOE
--------------------------------------------------------------------------
EEE (1) : EEE
EEO (2-4) : EEz EE+ EE-
EOE (5-7) : EzE E+E E-E
OEE (8-10) : zEE +EE -EE
EOO (11-13): Ezz E+- E-+
OEO (14-16): zEz +E- -E+
OOE (17-19): zzE +-E -+E
--------------------------------------------------------------------------
ENUM 4-Clusters: EEEE EEEO EEOE EOEE OEEE EEOO EOEO OEEO EOOE OEOE OOEE
--------------------------------------------------------------------------
EEEE (1) : EEEE
EEEO (2-4) : EEEz EEE+ EEE-
EEOE (5-7) : EEzE EE+E EE-E
EOEE (8-10) : EzEE E+EE E-EE
OEEE (11-13): zEEE +EEE -EEE
EEOO (14-16): EEzz EE+- EE-+
EOEO (17-19): EzEz E+E- -E+E
OEEO (20-22): zEEz +EE- -EE+
EOOE (23-25): EzzE E+-E E-+E
OEOE (26-28): zEzE +E-E -E+E
OOEE (29-31): zzEE +-EE -+EE
--------------------------------------------------------------------------
ENUM 5-Clusters
--------------------------------------------------------------------------
EEEEE (1) : EEEEE
EEEEO (2-4) : EEEEz EEEE+ EEEE-
EEEOE (5-7) : EEEzE EEE+E EEE-E
EEOEE (8-10) : EEzEE EE+EE EE-EE
EOEEE (11-13): EzEEE E+EEE E-EEE
OEEEE (14-16): zEEEE +EEEE -EEEE
EEEOO (17-19): EEEzz EEE+- EEE-+
EEOEO (20-22): EEzEz EE+E- EE-E+
EOEEO (23-25): EzEEz E+EE- E-EE+
OEEEO (26-28): zEEEz +EEE- -EEE+
EEOOE (29-31): EEzzE EE+-E EE-+E
EOEOE (32-34): EzEzE E+E-E E-E+E
EOEOE (35-37): zEEzE +EE-E -EE+E
EOOEE (38-40): EzzEE E+-EE E-+EE
OEOEE (41-43): zEzEE +E-EE -E+EE
OOEEE (44-46): zzEEE +-EEE -+EEE
--------------------------------------------------------------------------
ENUM 6-Clusters
--------------------------------------------------------------------------
EEEEEE (1) : EEEEEE
EEEEEO (2-4) : EEEEEz EEEEE+ EEEEE-
EEEEOE (5-7) : EEEEzE EEEE+E EEEE-E
EEEOEE (8-10) : EEEzEE EEE+EE EEE-EE
EEOEEE (11-13): EEzEEE EE+EEE EE-EEE
EOEEEE (14-16): EzEEEE +EEEEE -EEEEE
OEEEEE (17-19): zEEEEE +EEEEE -EEEEE
EEEEOO (20-22): EEEEzz EEEE+- EEEE-+
EEEOEO (23-25): EEEzEz EEE+E- EEE-E+
EEOEEO (26-28): EEzEEz EE+EE- EE-EE+
EOEEEO (29-31): EzEEEz E+EEE- E-EEE+
OEEEEO (32-34): zEEEEz +EEEE- -EEEE+
EEEOOE (35-37): EEEzzE EEE+-E EEE-+E
EEOEOE (38-40): EEzEzE EE+E-E EE-E+E
EOEEOE (41-43): EzEEzE E+EE-E E-EE+E
OEEEOE (44-46): zEEEzE +EEE-E -EEE+E
EEOOEE (47-49): EEzzEE EE+-EE EE-+EE
EOEOEE (50-51): EzEzEE E+E-EE E-E+EE
OEEOEE (53-55): zEEzEE +EE-EE -EE+EE
EOOEEE (56-58): EzzEEE E+-EEE E-+EEE
OEOEEE (59-61): zEzEEE +E-EEE -E+EEE
OOEEEE (62-64): zzEEEE +-EEEE -+EEEE
%}
function [z,r,l] = spinopidx(clusterSize,iSpin)
switch clusterSize
case 1
E = 1;
Z = 2; R = 3; L = 4;
zrl = [Z R L];
case 2
EE = 1;
EZ = 2; ER = 3; EL = 4;
ZE = 5; RE = 6; LE = 7;
switch iSpin
case 1, zrl = [ZE RE LE];
case 2, zrl = [EZ ER EL];
end
case 3
EEE = 1;
EEZ = 2; EER = 3; EEL = 4;
EZE = 5; ERE = 6; ELE = 7;
ZEE = 8; REE = 9; LEE = 10;
switch iSpin
case 3, zrl = [EEZ EER EEL];
case 2, zrl = [EZE ERE ELE];
case 1, zrl = [ZEE REE LEE];
end
case 4
EEEE = 1;
EEEZ = 2; EEER = 3; EEEL = 4;
EEZE = 5; EERE = 6; EELE = 7;
EZEE = 8; EREE = 9; ELEE = 10;
ZEEE = 11; REEE = 12; LEEE = 13;
switch iSpin
case 4, zrl = [EEEZ EEER EEEL];
case 3, zrl = [EEZE EERE EELE];
case 2, zrl = [EZEE EREE ELEE];
case 1, zrl = [ZEEE REEE LEEE];
end
case 5
EEEEE = 1;
EEEEZ = 2; EEEER = 3; EEEEL = 4;
EEEZE = 5; EEERE = 6; EEELE = 7;
EEZEE = 8; EEREE = 9; EELEE = 10;
EZEEE = 11; EREEE = 12; ELEEE = 13;
ZEEEE = 14; REEEE = 15; LEEEE = 16;
switch iSpin
case 5, zrl = [EEEEZ EEEER EEEEL];
case 4, zrl = [EEEZE EEERE EEELE];
case 3, zrl = [EEZEE EEREE EELEE];
case 2, zrl = [EZEEE EREEE ELEEE];
case 1, zrl = [ZEEEE REEEE LEEEE];
end
case 6
EEEEEE = 1;
EEEEEZ = 2; EEEEER = 3; EEEEEL = 4;
EEEEZE = 5; EEEERE = 6; EEEELE = 7;
EEEZEE = 8; EEEREE = 9; EEELEE = 10;
EEZEEE = 11; EEREEE = 12; EELEEE = 13;
EZEEEE = 14; EREEEE = 15; ELEEEE = 16;
ZEEEEE = 17; REEEEE = 18; LEEEEE = 19;
switch iSpin
case 6, zrl = [EEEEEZ EEEEER EEEEEL];
case 5, zrl = [EEEEZE EEEERE EEEELE];
case 4, zrl = [EEEZEE EEEREE EEELEE];
case 3, zrl = [EEZEEE EEREEE EELEEE];
case 2, zrl = [EZEEEE EREEEE ELEEEE];
case 1, zrl = [ZEEEEE REEEEE LEEEEE];
end
end
z = zrl(1);
r = zrl(2);
l = zrl(3);
end
function [zz,rl,lr,zr,zl,rz,lz,rr,ll] = spinopidx2(clusterSize,iSpin,jSpin)
switch clusterSize
case 2
ZZ = 8; RL = 9; LR = 10;
ZR = 11; ZL = 12; RZ = 13;
LZ = 14; RR = 15; LL = 16;
IJ = [ZZ RL LR ZR ZL RZ LZ RR LL];
case 3
EZZ = 11; ERL = 12; ELR = 13;
ZEZ = 14; REL = 15; LER = 16;
ZZE = 17; RLE = 18; LRE = 19;
EZR = 20; EZL = 21; ERZ = 22;
ELZ = 23; ZER = 24; ZEL = 25;
REZ = 26; LEZ = 27; ZRE = 28;
ZLE = 29; RZE = 30; LZE = 31;
ERR = 32; ELL = 33; RER = 34;
LEL = 35; RRE = 36; LLE = 37;
switch iSpin
case 1 % OOE or OEO
switch jSpin
case 3, IJ = [ZEZ REL LER ZER ZEL REZ LEZ RER LEL]; % OEO
case 2, IJ = [ZZE RLE LRE ZRE ZLE RZE LZE RRE LLE]; % OOE
end
case 2, IJ = [EZZ ERL ELR EZR EZL ERZ ELZ ERR ELL]; % EOO
end
case 4
EEZZ = 14; EERL = 15; EELR = 16;
EZEZ = 17; EREL = 18; ELER = 19;
ZEEZ = 20; REEL = 21; LEER = 22;
EZZE = 23; ERLE = 24; ELRE = 25;
ZEZE = 26; RELE = 27; LERE = 28;
ZZEE = 29; RLEE = 30; LREE = 31;
EEZR = 32; EEZL = 33; EERZ = 34; EELZ = 35;
EZER = 36; EZEL = 37; EREZ = 38; ELEZ = 39;
ZEER = 40; ZEEL = 41; REEZ = 42; LEEZ = 43;
EZRE = 44; EZLE = 45; ERZE = 46; ELZE = 47;
ZERE = 48; ZELE = 49; REZE = 50; LEZE = 51;
ZREE = 52; ZLEE = 53; RZEE = 54; LZEE = 55;
EERR = 56; EELL = 57;
ERER = 58; ELEL = 59;
REER = 60; LEEL = 61;
ERRE = 62; ELLE = 63;
RERE = 64; LELE = 65;
RREE = 66; LLEE = 67;
switch iSpin
case 1
switch jSpin
case 4, IJ = [ZEEZ REEL LEER ZEER ZEEL REEZ LEEZ REER LEEL]; % OEEO
case 3, IJ = [ZEZE RELE LERE ZERE ZELE REZE LEZE RERE LELE]; % OEOE
case 2, IJ = [ZZEE RLEE LREE ZREE ZLEE RZEE LZEE RREE LLEE]; % OOEE
end
case 2
switch jSpin
case 4, IJ = [EZEZ EREL ELER EZER EZEL EREZ ELEZ ERER ELEL]; % EOEO
case 3, IJ = [EZZE ERLE ELRE EZRE EZLE ERZE ELZE ERRE ELLE]; % EOOE
end
case 3, IJ = [EEZZ EERL EELR EEZR EEZL EERZ EELZ EERR EELL]; % EEOO
end
case 5
EEEZZ = 17; EEERL = 18; EEELR = 19;
EEZEZ = 20; EEREL = 21; EELER = 22;
EZEEZ = 23; EREEL = 24; ELEER = 25;
ZEEEZ = 26; REEEL = 27; LEEER = 28;
EEZZE = 29; EERLE = 30; EELRE = 31;
EZEZE = 32; ERELE = 33; ELERE = 34;
ZEEZE = 35; REELE = 36; LEERE = 37;
EZZEE = 38; ERLEE = 39; ELREE = 40;
ZEZEE = 41; RELEE = 42; LEREE = 43;
ZZEEE = 44; RLEEE = 45; LREEE = 46;
EEEZR = 47; EEEZL = 48; EEERZ = 49;
EEELZ = 50; EEZER = 51; EEZEL = 52;
EEREZ = 53; EELEZ = 54; EZEER = 55;
EZEEL = 56; EREEZ = 57; ELEEZ = 58;
ZEEER = 59; ZEEEL = 60; REEEZ = 61;
LEEEZ = 62; EEZRE = 63; EEZLE = 64;
EERZE = 65; EELZE = 66; EZERE = 67;
EZELE = 68; EREZE = 69; ELEZE = 70;
ZEERE = 71; ZEELE = 72; REEZE = 73;
LEEZE = 74; EZREE = 75; EZLEE = 76;
ERZEE = 77; ELZEE = 78; ZEREE = 79;
ZELEE = 80; REZEE = 81; LEZEE = 82;
ZREEE = 83; ZLEEE = 84; RZEEE = 85;
LZEEE = 86; EEERR = 87; EEELL = 88;
EERER = 89; EELEL = 90; EREER = 91;
ELEEL = 92; REEER = 93; LEEEL = 94;
EERRE = 95; EELLE = 96; ERERE = 97;
ELELE = 98; REERE = 99; LEELE = 100;
ERREE = 101; ELLEE = 102; REREE = 103;
LELEE = 104; RREEE = 105; LLEEE = 106;
switch iSpin
case 1
switch jSpin
case 5, IJ = [ZEEEZ REEEL LEEER ZEEER ZEEEL REEEZ LEEEZ REEER LEEEL]; % OEEEO
case 4, IJ = [ZEEZE REELE LEERE ZEERE ZEELE REEZE LEEZE REERE LEELE]; % OEEOE
case 3, IJ = [ZEZEE RELEE LEREE ZEREE ZELEE REZEE LEZEE REREE LELEE]; % OEOEE
case 2, IJ = [ZZEEE RLEEE LREEE ZREEE ZLEEE RZEEE LZEEE RREEE LLEEE]; % OOEEE
end
case 2
switch jSpin
case 5, IJ = [EZEEZ EREEL ELEER EZEER EZEEL EREEZ ELEEZ EREER ELEEL]; % EOEEO
case 4, IJ = [EZEZE ERELE ELERE EZERE EZELE EREZE ELEZE ERERE ELELE]; % EOEOE
case 3, IJ = [EZZEE ERLEE ELREE EZREE EZLEE ERZEE ELZEE ERREE ELLEE]; % EOOEE
end
case 3
switch jSpin
case 5, IJ = [EEZEZ EEREL EELER EEZER EEZEL EEREZ EELEZ EERER EELEL]; % EEOEO
case 4, IJ = [EEZZE EERLE EELRE EEZRE EEZLE EERZE EELZE EERRE EELLE]; % EEOOE
end
case 4, IJ = [EEEZZ EEERL EEELR EEEZR EEEZL EEERZ EEELZ EEERR EEELL]; % EEEOO
end
case 6
EEEEZZ = 20; EEEERL = 21; EEEELR = 22;
EEEZEZ = 23; EEEREL = 24; EEELER = 25;
EEZEEZ = 26; EEREEL = 27; EELEER = 28;
EZEEEZ = 29; EREEEL = 30; ELEEER = 31;
ZEEEEZ = 32; REEEEL = 33; LEEEER = 34;
EEEZZE = 35; EEERLE = 36; EEELRE = 37;
EEZEZE = 38; EERELE = 39; EELERE = 40;
EZEEZE = 41; EREELE = 42; ELEERE = 43;
ZEEEZE = 44; REEELE = 45; LEEERE = 46;
EEZZEE = 47; EERLEE = 48; EELREE = 49;
EZEZEE = 50; ERELEE = 51; ELEREE = 52;
ZEEZEE = 53; REELEE = 54; LEEREE = 55;
EZZEEE = 56; ERLEEE = 57; ELREEE = 58;
ZEZEEE = 59; RELEEE = 60; LEREEE = 61;
ZZEEEE = 62; RLEEEE = 63; LREEEE = 64;
EEEEZR = 65; EEEEZL = 66; EEEERZ = 67;
EEEELZ = 68; EEEZER = 69; EEEZEL = 70;
EEEREZ = 71; EEELEZ = 72; EEZEER = 73;
EEZEEL = 74; EEREEZ = 75; EELEEZ = 76;
EZEEER = 77; EZEEEL = 78; EREEEZ = 79;
ELEEEZ = 80; ZEEEER = 81; ZEEEEL = 82;
REEEEZ = 83; LEEEEZ = 84; EEEZRE = 85;
EEEZLE = 86; EEERZE = 87; EEELZE = 88;
EEZERE = 89; EEZELE = 90; EEREZE = 91;
EELEZE = 92; EZEERE = 93; EZEELE = 94;
EREEZE = 95; ELEEZE = 96; ZEEERE = 97;
ZEEELE = 98; REEEZE = 99; LEEEZE = 100;
EEZREE = 101; EEZLEE = 102; EERZEE = 103;
EELZEE = 104; EZEREE = 105; EZELEE = 106;
EREZEE = 107; ELEZEE = 108; ZEEREE = 109;
ZEELEE = 110; REEZEE = 111; LEEZEE = 112;
EZREEE = 113; EZLEEE = 114; ERZEEE = 115;
ELZEEE = 116; ZEREEE = 117; ZELEEE = 118;
REZEEE = 119; LEZEEE = 120; ZREEEE = 121;
ZLEEEE = 122; RZEEEE = 123; LZEEEE = 124;
EEEERR = 125; EEEELL = 126; EEERER = 127;
EEELEL = 128; EEREER = 129; EELEEL = 130;
EREEER = 131; ELEEEL = 132; REEEER = 133;
LEEEEL = 134; EEERRE = 135; EEELLE = 136;
EERERE = 137; EELELE = 138; EREERE = 139;
ELEELE = 140; REEERE = 141; LEEELE = 142;
EERREE = 143; EELLEE = 144; EREREE = 145;
ELELEE = 146; REEREE = 147; LEELEE = 148;
ERREEE = 149; ELLEEE = 150; REREEE = 151;
LELEEE = 152; RREEEE = 153; LLEEEE = 154;
switch iSpin
case 1
switch jSpin
case 6, IJ = [ZEEEEZ REEEEL LEEEER ZEEEER ZEEEEL REEEEZ LEEEEZ REEEER LEEEEL]; % OEEEEO
case 5, IJ = [ZEEEZE REEELE LEEERE ZEEERE ZEEELE REEEZE LEEEZE REEERE LEEELE]; % OEEEOE
case 4, IJ = [ZEEZEE REELEE LEEREE ZEEREE ZEELEE REEZEE LEEZEE REEREE LEELEE]; % OEEOEE
case 3, IJ = [ZEZEEE RELEEE LEREEE ZEREEE ZELEEE REZEEE LEZEEE REREEE LELEEE]; % OEOEEE
case 2, IJ = [ZZEEEE RLEEEE LREEEE ZREEEE ZLEEEE RZEEEE LZEEEE RREEEE LLEEEE]; % OOEEEE
end
case 2
switch jSpin
case 6, IJ = [EZEEEZ EREEEL ELEEER EZEEER EZEEEL EREEEZ ELEEEZ EREEER ELEEEL]; % EOEEEO
case 5, IJ = [EZEEZE EREELE ELEERE EZEERE EZEELE EREEZE ELEEZE EREERE ELEELE]; % EOEEOE
case 4, IJ = [EZEZEE ERELEE ELEREE EZEREE EZELEE EREZEE ELEZEE EREREE ELELEE]; % EOEOEE
case 3, IJ = [EZZEEE ERLEEE ELREEE EZREEE EZLEEE ERZEEE ELZEEE ERREEE ELLEEE]; % EOOEEE
end
case 3
switch jSpin
case 6, IJ = [EEZEEZ EEREEL EELEER EEZEER EEZEEL EEREEZ EELEEZ EEREER EELEEL]; % EEOEEO
case 5, IJ = [EEZEZE EERELE EELERE EEZERE EEZELE EEREZE EELEZE EERERE EELELE]; % EEOEOE
case 4, IJ = [EEZZEE EERLEE EELREE EEZREE EEZLEE EERZEE EELZEE EERREE EELLEE]; % EEOOEE
end
case 4
switch jSpin
case 6, IJ = [EEEZEZ EEEREL EEELER EEEZER EEEZEL EEEREZ EEELEZ EEERER EEELEL]; % EEEOEO
case 5, IJ = [EEEZZE EEERLE EEELRE EEEZRE EEEZLE EEERZE EEELZE EEERRE EEELLE]; % EEEOOE
end
case 5, IJ = [EEEEZZ EEEERL EEEELR EEEEZR EEEEZL EEEERZ EEEELZ EEEERR EEEELL]; % EEEEOO
end
end
% 1 2 3 4 5 6 7 8 9
% [ZZ RL LR ZR ZL RZ LZ RR LL]
zz = IJ(1);
rl = IJ(2); lr = IJ(3);
zr = IJ(4); zl = IJ(5);
rz = IJ(6); lz = IJ(7);
rr = IJ(8); ll = IJ(9);
end
function [xx,xy,xz,yx,yy,yz,zx,zy,zz] = spinopidx_nq(iSpin)
% ENUM for spin-operator indices.
XX_ = 1; XY_ = 4; XZ_ = 7;
YX_ = 2; YY_ = 5; YZ_ = 8;
ZX_ = 3; ZY_ = 6; ZZ_ = 9;
off = (iSpin-1)*9;
xx = XX_ + off;
xy = XY_ + off;
xz = XZ_ + off;
yx = YX_ + off;
yy = YY_ + off;
yz = YZ_ + off;
zx = ZX_ + off;
zy = ZY_ + off;
zz = ZZ_ + off;
end