-
Notifications
You must be signed in to change notification settings - Fork 1
Expand file tree
/
Copy pathextended_SSH.nb
More file actions
3280 lines (3220 loc) · 162 KB
/
Copy pathextended_SSH.nb
File metadata and controls
3280 lines (3220 loc) · 162 KB
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
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 12.3' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 162710, 3272]
NotebookOptionsPosition[ 158284, 3194]
NotebookOutlinePosition[ 158695, 3211]
CellTagsIndexPosition[ 158652, 3208]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["Tight binding of an extended SSH Model", "Subtitle",
CellChangeTimes->{{3.85288256747455*^9, 3.8528825964466105`*^9}, {
3.853909726539834*^9,
3.853909728923129*^9}},ExpressionUUID->"47842df3-cef7-48c3-abf5-\
a5e93fe31b0e"],
Cell[CellGroupData[{
Cell["Lattice configuration", "Section",
CellChangeTimes->{{3.852882603390766*^9,
3.8528826116926155`*^9}},ExpressionUUID->"295963f2-c0fa-43ae-a2e7-\
f2fc825b69d9"],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{"lattice", "[", "num_", "]"}], ":=",
RowBox[{"Module", "[",
RowBox[{
RowBox[{"{",
RowBox[{
"atom1", ",", "atom2", ",", "t11", ",", "t12", ",", "t21", ",", "t22"}],
"}"}], ",",
RowBox[{
RowBox[{"atom1", "=",
RowBox[{
RowBox[{
RowBox[{"Sphere", "[",
RowBox[{"#", ",", "0.2"}], "]"}], "&"}], "/@",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{"x", ",", "0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",", "num"}], "}"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"atom2", "=",
RowBox[{
RowBox[{
RowBox[{"Sphere", "[",
RowBox[{"#", ",", "0.2"}], "]"}], "&"}], "/@",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"x", "+",
RowBox[{"1", "/", "2"}]}], ",",
RowBox[{
RowBox[{"Sqrt", "[", "3", "]"}], "/", "2"}], ",", "0"}], "}"}],
",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",", "num"}], "}"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"t11", "=",
RowBox[{
RowBox[{
RowBox[{"Cylinder", "[",
RowBox[{"#", ",", "0.05"}], "]"}], "&"}], "/@",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"x", ",", "0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"x", "+",
FractionBox["1", "2"]}], ",",
FractionBox[
SqrtBox["3"], "2"], ",", "0"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",", "num"}], "}"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"t12", "=",
RowBox[{
RowBox[{
RowBox[{"Cylinder", "[",
RowBox[{"#", ",", "0.05"}], "]"}], "&"}], "/@",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"x", "+",
RowBox[{"1", "/", "2"}]}], ",",
FractionBox[
SqrtBox["3"], "2"], ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"x", "+", "1"}], ",", "0", ",", "0"}], "}"}]}], "}"}],
",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",",
RowBox[{"num", "-", "1"}]}], "}"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"t21", "=",
RowBox[{
RowBox[{
RowBox[{"Cylinder", "[",
RowBox[{"#", ",", "0.05"}], "]"}], "&"}], "/@",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"x", ",", "0", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"x", "+",
FractionBox["3", "2"]}], ",",
FractionBox[
SqrtBox["3"], "2"], ",", "0"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",",
RowBox[{"num", "-", "1"}]}], "}"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"t22", "=",
RowBox[{
RowBox[{
RowBox[{"Cylinder", "[",
RowBox[{"#", ",", "0.05"}], "]"}], "&"}], "/@",
RowBox[{"Table", "[",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{
RowBox[{"x", "+",
FractionBox["1", "2"]}], ",",
FractionBox[
SqrtBox["3"], "2"], ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"x", "+",
FractionBox["4", "2"]}], ",", "0", ",", "0"}], "}"}]}], "}"}],
",",
RowBox[{"{",
RowBox[{"x", ",", "0", ",",
RowBox[{"num", "-", "2"}]}], "}"}]}], "]"}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"Graphics3D", "[",
RowBox[{
RowBox[{"{",
RowBox[{
"Red", ",", "atom1", ",", "Green", ",", "atom2", ",", "Black", ",",
"t11", ",", "Orange", ",", "t12", ",", "Blue", ",", "t21", ",",
"LightCyan", ",", "t22"}], "}"}], ",",
RowBox[{"Boxed", "\[Rule]", "False"}], ",",
RowBox[{"ViewPoint", "\[Rule]", "Above"}]}], "]"}]}]}],
"]"}]}], "\[IndentingNewLine]",
RowBox[{"lattice", "[", "7", "]"}], "\[IndentingNewLine]"}], "Input",
CellChangeTimes->{{3.852882616909848*^9, 3.8528826602824955`*^9}, {
3.8528827099376864`*^9, 3.8528830155265713`*^9}, {3.8528831479769177`*^9,
3.852883182170124*^9}, {3.8528832856534376`*^9, 3.852883303570341*^9}, {
3.8528834017360954`*^9, 3.852883452820835*^9}, {3.852883560798036*^9,
3.8528835741044197`*^9}, {3.852883611674282*^9, 3.8528836640016017`*^9}, {
3.852883719822345*^9, 3.8528840057860594`*^9}, {3.8528840367160206`*^9,
3.852884180984445*^9}, {3.852884285152846*^9, 3.85288458462499*^9}, {
3.8528846308767953`*^9, 3.8528846642600203`*^9}, 3.852884707596814*^9},
CellLabel->"In[36]:=",ExpressionUUID->"dfeac751-8d92-49cb-9f84-e1768b7d77a4"],
Cell[BoxData[
Graphics3DBox[{
{RGBColor[1, 0, 0], SphereBox[{0, 0, 0}, 0.2], SphereBox[{1, 0, 0}, 0.2],
SphereBox[{2, 0, 0}, 0.2], SphereBox[{3, 0, 0}, 0.2],
SphereBox[{4, 0, 0}, 0.2], SphereBox[{5, 0, 0}, 0.2],
SphereBox[{6, 0, 0}, 0.2], SphereBox[{7, 0, 0}, 0.2]},
{RGBColor[0, 1, 0],
SphereBox[
NCache[{Rational[1, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {
0.5, 0.8660254037844386, 0}], 0.2],
SphereBox[
NCache[{Rational[3, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {
1.5, 0.8660254037844386, 0}], 0.2],
SphereBox[
NCache[{Rational[5, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {
2.5, 0.8660254037844386, 0}], 0.2],
SphereBox[
NCache[{Rational[7, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {
3.5, 0.8660254037844386, 0}], 0.2],
SphereBox[
NCache[{Rational[9, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {
4.5, 0.8660254037844386, 0}], 0.2],
SphereBox[
NCache[{Rational[11, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {
5.5, 0.8660254037844386, 0}], 0.2],
SphereBox[
NCache[{Rational[13, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {
6.5, 0.8660254037844386, 0}], 0.2],
SphereBox[
NCache[{Rational[15, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {
7.5, 0.8660254037844386, 0}], 0.2]},
{GrayLevel[0],
CylinderBox[
NCache[{{0, 0, 0}, {
Rational[1, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{0, 0, 0}, {
0.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{1, 0, 0}, {
Rational[3, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{1, 0, 0}, {
1.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{2, 0, 0}, {
Rational[5, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{2, 0, 0}, {
2.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{3, 0, 0}, {
Rational[7, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{3, 0, 0}, {
3.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{4, 0, 0}, {
Rational[9, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{4, 0, 0}, {
4.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{5, 0, 0}, {
Rational[11, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{5, 0, 0}, {
5.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{6, 0, 0}, {
Rational[13, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{6, 0, 0}, {
6.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{7, 0, 0}, {
Rational[15, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{7, 0, 0}, {
7.5, 0.8660254037844386, 0}}], 0.05]},
{RGBColor[1, 0.5, 0],
CylinderBox[
NCache[{{Rational[1, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {1, 0,
0}}, {{0.5, 0.8660254037844386, 0}, {1, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[3, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {2, 0,
0}}, {{1.5, 0.8660254037844386, 0}, {2, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[5, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {3, 0,
0}}, {{2.5, 0.8660254037844386, 0}, {3, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[7, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {4, 0,
0}}, {{3.5, 0.8660254037844386, 0}, {4, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[9, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {5, 0,
0}}, {{4.5, 0.8660254037844386, 0}, {5, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[11, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {6, 0,
0}}, {{5.5, 0.8660254037844386, 0}, {6, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[13, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {7, 0,
0}}, {{6.5, 0.8660254037844386, 0}, {7, 0, 0}}], 0.05]},
{RGBColor[0, 0, 1],
CylinderBox[
NCache[{{0, 0, 0}, {
Rational[3, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{0, 0, 0}, {
1.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{1, 0, 0}, {
Rational[5, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{1, 0, 0}, {
2.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{2, 0, 0}, {
Rational[7, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{2, 0, 0}, {
3.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{3, 0, 0}, {
Rational[9, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{3, 0, 0}, {
4.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{4, 0, 0}, {
Rational[11, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{4, 0, 0}, {
5.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{5, 0, 0}, {
Rational[13, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{5, 0, 0}, {
6.5, 0.8660254037844386, 0}}], 0.05],
CylinderBox[
NCache[{{6, 0, 0}, {
Rational[15, 2], Rational[1, 2] 3^Rational[1, 2], 0}}, {{6, 0, 0}, {
7.5, 0.8660254037844386, 0}}], 0.05]},
{RGBColor[0.9, 1, 1],
CylinderBox[
NCache[{{Rational[1, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {2, 0,
0}}, {{0.5, 0.8660254037844386, 0}, {2, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[3, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {3, 0,
0}}, {{1.5, 0.8660254037844386, 0}, {3, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[5, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {4, 0,
0}}, {{2.5, 0.8660254037844386, 0}, {4, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[7, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {5, 0,
0}}, {{3.5, 0.8660254037844386, 0}, {5, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[9, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {6, 0,
0}}, {{4.5, 0.8660254037844386, 0}, {6, 0, 0}}], 0.05],
CylinderBox[
NCache[{{Rational[11, 2], Rational[1, 2] 3^Rational[1, 2], 0}, {7, 0,
0}}, {{5.5, 0.8660254037844386, 0}, {7, 0, 0}}], 0.05]}},
Boxed->False,
ViewPoint->Above]], "Output",
CellChangeTimes->{
3.8528838760284457`*^9, 3.852884006586644*^9, 3.852884039767247*^9, {
3.852884169180587*^9, 3.852884181501731*^9}, 3.8528842869450893`*^9, {
3.852884447385615*^9, 3.8528844538408923`*^9}, 3.8528845867959275`*^9, {
3.8528846440225897`*^9, 3.8528846665896916`*^9}, 3.8528847083380375`*^9,
3.8544392122064075`*^9, 3.8544984986521025`*^9},
CellLabel->"Out[37]=",ImageCache->GraphicsData["CompressedBitmap", "\<\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\
\>", "ImageResolution" -> \
72.],ExpressionUUID->"20356e51-8be0-4343-ac27-019244496e0c"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Bulk Hamiltonian", "Section",
CellChangeTimes->{{3.8529595734195814`*^9, 3.852959578276229*^9}, {
3.852959611015812*^9,
3.85295961150308*^9}},ExpressionUUID->"bfd070e4-5719-4350-94d3-\
25ec4e23a99f"],
Cell[BoxData[
RowBox[{
RowBox[{"hamiltonian", "[",
RowBox[{"kx_", ",", "w_"}], "]"}], ":=",
RowBox[{"Module", "[",
RowBox[{
RowBox[{"{",
RowBox[{
"t11", ",", "t12", ",", "t21", ",", "t22", ",", "h12", ",", "h21", ",",
"ham"}], "}"}], ",", "\[IndentingNewLine]",
RowBox[{
RowBox[{"t11", "=",
RowBox[{
RowBox[{"-", "1"}], "+", "w"}]}], ";", "\[IndentingNewLine]",
RowBox[{"t12", "=",
RowBox[{
RowBox[{"-", "1"}], "-", "w"}]}], ";", "\[IndentingNewLine]",
RowBox[{"t21", "=",
RowBox[{"t2", "+", "ww"}]}], ";", "\[IndentingNewLine]",
RowBox[{"t22", "=",
RowBox[{"t2", "-", "ww"}]}], ";", "\[IndentingNewLine]",
RowBox[{"h12", "=",
RowBox[{"t11", "+",
RowBox[{"t12", "*",
RowBox[{"Exp", "[",
RowBox[{
RowBox[{"-", "\[ImaginaryI]"}], " ", "kx"}], "]"}]}], "+",
RowBox[{"t21", "*",
RowBox[{"Exp", "[",
RowBox[{
RowBox[{"-", "2"}], "\[ImaginaryI]", " ", "kx"}], "]"}]}], "+",
RowBox[{"t22", "*",
RowBox[{"Exp", "[",
RowBox[{"\[ImaginaryI]", " ", "kx"}], "]"}]}]}]}], ";",
"\[IndentingNewLine]",
RowBox[{"h21", "=",
RowBox[{"Conjugate", "[", "h12", "]"}]}], ";", "\[IndentingNewLine]",
RowBox[{"ham", "=",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"0", ",", "h12"}], "}"}], ",",
RowBox[{"{",
RowBox[{"h21", ",", "0"}], "}"}]}], "}"}]}], ";",
"\[IndentingNewLine]",
RowBox[{"Return", "[", "ham", "]"}], ";"}]}], "\[IndentingNewLine]",
"]"}]}]], "Input",
CellChangeTimes->{{3.852958493889432*^9, 3.8529585193598814`*^9}, {
3.8529585744439507`*^9, 3.8529585912590637`*^9}, {3.852958643360838*^9,
3.8529588482448125`*^9}, {3.8529605288354516`*^9, 3.8529605302217884`*^9}, {
3.8529629301746626`*^9, 3.8529629860733094`*^9}, {3.8529630681156535`*^9,
3.852963103214485*^9}},
CellLabel->"In[38]:=",ExpressionUUID->"70369161-817b-4c59-95db-c9b0df508b91"],
Cell[BoxData[
RowBox[{
RowBox[{"el", "=",
RowBox[{"ParallelTable", "[",
RowBox[{
RowBox[{"Eigenvalues", "[",
RowBox[{
RowBox[{"hamiltonian", "[",
RowBox[{"kx", ",",
RowBox[{"-", "0.5"}]}], "]"}], "/.",
RowBox[{"{",
RowBox[{
RowBox[{"kx", "->", "kk"}], ",",
RowBox[{"t2", "->",
RowBox[{"-", "5"}]}], ",",
RowBox[{"ww", "->",
RowBox[{"-", "2.5"}]}]}], "}"}]}], "]"}], ",",
RowBox[{"{",
RowBox[{"kk", ",",
RowBox[{"-", "\[Pi]"}], ",", "\[Pi]", ",",
RowBox[{"0.01", "\[Pi]"}]}], "}"}]}], "]"}]}], ";"}]], "Input",
CellChangeTimes->{{3.8529588592602797`*^9, 3.852958914497547*^9}, {
3.8529589451831455`*^9, 3.852959034211105*^9}, {3.8529591455469255`*^9,
3.852959148159213*^9}, {3.8529592446422405`*^9, 3.852959249736701*^9}, {
3.852959300550104*^9, 3.852959302529157*^9}, 3.852959404134194*^9,
3.8529595979851117`*^9, {3.852960537794428*^9, 3.8529605517729073`*^9}, {
3.8529629941642756`*^9, 3.8529630065206175`*^9}},
CellLabel->"In[39]:=",ExpressionUUID->"eabe356d-d804-448c-bfe4-d1e0146223cd"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"ListPlot", "[",
RowBox[{
RowBox[{"Transpose", "@",
RowBox[{"Re", "[", "el", "]"}]}], ",",
RowBox[{"Joined", "\[Rule]", "True"}], ",",
RowBox[{"DataRange", "\[Rule]",
RowBox[{"{",
RowBox[{
RowBox[{"-", "\[Pi]"}], ",", "\[Pi]"}], "}"}]}], ",",
RowBox[{"AspectRatio", "\[Rule]", "1"}], ",",
RowBox[{"Frame", "->", "True"}], ",",
RowBox[{"ColorFunction", "\[Rule]", "\"\<Rainbow\>\""}]}], "]"}]], "Input",
CellChangeTimes->{{3.852959059637041*^9, 3.85295906150559*^9}, {
3.852959098400404*^9, 3.852959099823586*^9}, {3.852959222812791*^9,
3.852959226120063*^9}, 3.8529593090477853`*^9, {3.8529593455374837`*^9,
3.85295934896854*^9}, {3.852959431725368*^9, 3.8529595453850794`*^9}, {
3.852959724305982*^9, 3.852959736512499*^9}, {3.8529599507324286`*^9,
3.8529599589600434`*^9}, {3.8529599998618064`*^9, 3.8529601013836083`*^9}},
CellLabel->"In[40]:=",ExpressionUUID->"2b2780e9-81eb-48c6-a4b9-2d0c12e6bb23"],
Cell[BoxData[
GraphicsBox[{{}, GraphicsComplexBox[CompressedData["
1:eJzt2f1XlVUWB/ALCKJBBr7ci1zo3isKmmKlGJp6vstcVo4WGooimWVM+Iaa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"], {{}, {},
{RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.007333333333333334],
AbsoluteThickness[1.6],
LineBox[{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},
VertexColors->Automatic]},
{RGBColor[0.880722, 0.611041, 0.142051], PointSize[0.007333333333333334],
AbsoluteThickness[1.6], LineBox[CompressedData["
1:eJwV0mdbDQAAgNF7yS47ISsjI2STbBmFkD3jZo8iI0V2KLt/lVD2XpGRyKyM
cHw4P+B9njcmlJWWGQwEAiVcoZSrXOM6ZZRzg5vc4jZ3uMs97vOAhzziMU94
yjOe84IKXvKKSl7zhre8o4r3VPOBj9Twic984Svf+E4tddTzg5/84jcN/OEv
AYFBGtGYMJrQlGY0pwUtaUU4EbSmDW1pR3s60JFIOhFFZ7rQlWi60Z0e9KQX
MfSmD33pRyz9GcBABhHHYIYwlHiGMZwRjGQUoxnDWMaRwHgSmcBEJjGZKUxl
GtNJYgYzmcVskklhDnOZRyrzWcBC0ljEYpawlGUsZwUrWcVq1rCWdNaxnhAZ
bGAjm9jMFrayje3sYCf/x8xiF7vJZg972cd+cjhALnkc5BD5HOYIRznGcU5w
kgJOcZozFFLEWc5xngtc5BKXKeYfhztdLg==
"],
VertexColors->Automatic]}},
VertexColors->CompressedData["
1:eJztmnlUzP37xhNlp/DYKqJEksheuCxJGypakDVFlpKlxRJPPCgkEkWobFkq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