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hamiltonian_gap_data.jl
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hamiltonian_gap_data.jl
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n = 10;
k = 15;
Hnom = [
-0.8651 -1.8523 0.4197 -0.1122 -2.7506 0.1803 1.1892 0.5313 0.9505 0.5645;
-1.8523 1.4516 -1.9245 2.8732 0.1209 0.7284 0.7489 -0.1964 0.7034 -0.7444;
0.4197 -1.9245 1.4286 2.4392 -1.7482 1.3657 2.3490 -1.9712 -0.5001 -0.0643;
-0.1122 2.8732 2.4392 1.4238 2.7054 2.3610 -0.6832 -1.4983 -1.0119 -0.7163;
-2.7506 0.1209 -1.7482 2.7054 -1.6102 1.1200 0.6475 -2.3970 -1.9586 0.3845;
0.1803 0.7284 1.3657 2.3610 1.1200 -1.2872 1.2760 -1.2431 0.2184 -0.9981;
1.1892 0.7489 2.3490 -0.6832 0.6475 1.2760 1.4619 0.6963 -0.9674 1.4583;
0.5313 -0.1964 -1.9712 -1.4983 -2.3970 -1.2431 0.6963 0.6296 0.7015 0.2180;
0.9505 0.7034 -0.5001 -1.0119 -1.9586 0.2184 -0.9674 0.7015 2.1646 -0.9532;
0.5645 -0.7444 -0.0643 -0.7163 0.3845 -0.9981 1.4583 0.2180 -0.9532 -0.5312;
];
Hpert = cell(15);
Hpert[1] = [
-2.3756 -3.3882 1.1150 0.2871 -0.0032 0.1142 0.4908 0.0145 -1.4121 1.1788
-3.3882 -2.1118 2.1289 0.2874 -2.0609 -0.1065 -2.0319 -2.9297 0.1099 1.6614
1.1150 2.1289 -2.3356 -1.4504 0.2353 -0.7279 -1.2836 0.8526 0.7395 1.3122
0.2871 0.2874 -1.4504 2.6792 1.7780 0.8834 0.5105 -1.3658 0.8202 0.4316
-0.0032 -2.0609 0.2353 1.7780 -1.0930 -0.9964 0.2891 -0.3615 -2.2115 0.6632
0.1142 -0.1065 -0.7279 0.8834 -0.9964 -0.8695 0.4736 0.3008 -1.6291 -1.6872
0.4908 -2.0319 -1.2836 0.5105 0.2891 0.4736 -0.4074 -1.7655 1.1704 0.4532
0.0145 -2.9297 0.8526 -1.3658 -0.3615 0.3008 -1.7655 -0.8586 -0.3340 -0.5790
-1.4121 0.1099 0.7395 0.8202 -2.2115 -1.6291 1.1704 -0.3340 -2.7625 1.5058
1.1788 1.6614 1.3122 0.4316 0.6632 -1.6872 0.4532 -0.5790 1.5058 -2.2324
];
Hpert[2] = [
1.2705 -1.2327 -0.4670 -0.6197 0.5715 -1.0144 -1.0343 -0.5669 0.7431 1.2234
-1.2327 -4.6504 -1.4137 1.7238 -0.1182 0.5981 -0.3893 -1.8773 -0.8901 -1.2846
-0.4670 -1.4137 3.0420 -0.1168 0.9512 -0.4345 1.0802 -2.0395 -0.9306 1.8851
-0.6197 1.7238 -0.1168 1.7783 3.5857 1.7381 -0.7239 0.5660 0.0657 -1.3647
0.5715 -0.1182 0.9512 3.5857 3.7268 -0.7972 0.0921 -1.7490 0.7518 -3.7741
-1.0144 0.5981 -0.4345 1.7381 -0.7972 -0.2663 -1.2713 -2.8382 -0.3870 2.0510
-1.0343 -0.3893 1.0802 -0.7239 0.0921 -1.2713 -0.4989 -0.6246 0.2358 -1.3385
-0.5669 -1.8773 -2.0395 0.5660 -1.7490 -2.8382 -0.6246 -0.8033 1.4517 -1.2352
0.7431 -0.8901 -0.9306 0.0657 0.7518 -0.3870 0.2358 1.4517 -1.0956 0.8812
1.2234 -1.2846 1.8851 -1.3647 -3.7741 2.0510 -1.3385 -1.2352 0.8812 2.5396
];
Hpert[3] = [
-1.7921 0.2420 0.6979 -0.3519 0.5290 0.4255 -0.4450 1.0192 0.4265 1.6553
0.2420 3.6964 -0.9974 2.8489 0.4279 -0.6641 -2.3690 1.3639 2.1868 0.3970
0.6979 -0.9974 -1.4430 1.1089 -0.0682 -0.2188 2.3978 2.2567 -1.5213 1.0904
-0.3519 2.8489 1.1089 0.6542 -0.2936 -1.2680 -3.3583 -0.7827 -0.1497 -2.2984
0.5290 0.4279 -0.0682 -0.2936 -0.6607 0.3078 -0.4488 -0.3883 -0.2556 1.5204
0.4255 -0.6641 -0.2188 -1.2680 0.3078 0.0824 -1.2624 -0.2881 -2.4964 1.7696
-0.4450 -2.3690 2.3978 -3.3583 -0.4488 -1.2624 3.2395 0.3884 0.7814 -1.7613
1.0192 1.3639 2.2567 -0.7827 -0.3883 -0.2881 0.3884 -1.1447 0.1292 -1.4494
0.4265 2.1868 -1.5213 -0.1497 -0.2556 -2.4964 0.7814 0.1292 -2.4551 -0.8555
1.6553 0.3970 1.0904 -2.2984 1.5204 1.7696 -1.7613 -1.4494 -0.8555 -2.1081
];
Hpert[4] = [
-0.1431 1.1356 2.7541 -1.1946 -1.3246 1.5172 -0.0653 -0.4307 -1.7523 1.0293
1.1356 0.5370 1.9448 -1.8866 0.7684 0.6029 -1.7781 0.7189 1.0505 0.7786
2.7541 1.9448 -1.8189 -2.5142 1.6815 -0.1104 -0.2158 -0.7895 -1.4768 -1.6414
-1.1946 -1.8866 -2.5142 1.5118 -0.6013 -2.0505 1.4064 -0.4957 1.4458 -1.6632
-1.3246 0.7684 1.6815 -0.6013 -1.9280 -1.8710 -1.1968 0.3127 -0.3868 -0.8197
1.5172 0.6029 -0.1104 -2.0505 -1.8710 -0.8418 -1.8485 0.2943 -1.6591 0.8479
-0.0653 -1.7781 -0.2158 1.4064 -1.1968 -1.8485 -0.2871 -1.1267 -0.4745 -0.5978
-0.4307 0.7189 -0.7895 -0.4957 0.3127 0.2943 -1.1267 1.1697 -1.8231 0.6652
-1.7523 1.0505 -1.4768 1.4458 -0.3868 -1.6591 -0.4745 -1.8231 0.7332 -1.3198
1.0293 0.7786 -1.6414 -1.6632 -0.8197 0.8479 -0.5978 0.6652 -1.3198 -0.1291
];
Hpert[5] = [
-2.8880 0.7042 -1.2407 -0.9757 -0.7164 0.9147 -0.1483 0.8619 1.5960 -0.6320
0.7042 -1.6152 0.3049 -1.1793 -1.8731 -1.8635 -0.6633 0.4877 -1.0456 0.0199
-1.2407 0.3049 4.4737 1.3236 0.8130 -0.6212 -0.1396 0.6741 2.0102 2.7344
-0.9757 -1.1793 1.3236 2.4318 0.0103 0.3072 -1.5635 -1.4942 1.0417 1.2218
-0.7164 -1.8731 0.8130 0.0103 0.1670 0.0890 -0.0011 1.3752 -1.3021 -2.6859
0.9147 -1.8635 -0.6212 0.3072 0.0890 1.1171 0.3212 -1.0539 -1.4476 -0.7397
-0.1483 -0.6633 -0.1396 -1.5635 -0.0011 0.3212 0.2944 -0.4523 -3.3884 -1.4077
0.8619 0.4877 0.6741 -1.4942 1.3752 -1.0539 -0.4523 1.7842 2.5041 -0.9596
1.5960 -1.0456 2.0102 1.0417 -1.3021 -1.4476 -3.3884 2.5041 -0.4970 -1.8429
-0.6320 0.0199 2.7344 1.2218 -2.6859 -0.7397 -1.4077 -0.9596 -1.8429 1.4384
];
Hpert[6] = [
2.2835 0.5990 3.4777 -0.9529 -0.0681 0.8251 -0.3512 -0.1139 0.6734 0.1537
0.5990 1.5563 0.0738 0.6000 1.6135 0.8073 -0.7476 1.7298 -1.1902 -0.1440
3.4777 0.0738 -1.8746 0.1091 2.0512 0.2585 2.3314 0.1235 0.7790 1.0096
-0.9529 0.6000 0.1091 -1.3710 -0.0892 -1.5108 -1.4525 0.9204 -1.1727 -3.1071
-0.0681 1.6135 2.0512 -0.0892 -0.0746 -1.9857 -0.6944 0.5712 -0.2255 -0.1535
0.8251 0.8073 0.2585 -1.5108 -1.9857 -1.9067 -0.5301 1.0040 -1.7480 0.7281
-0.3512 -0.7476 2.3314 -1.4525 -0.6944 -0.5301 4.3529 0.3179 0.6217 1.1808
-0.1139 1.7298 0.1235 0.9204 0.5712 1.0040 0.3179 0.2559 -1.4798 -0.8466
0.6734 -1.1902 0.7790 -1.1727 -0.2255 -1.7480 0.6217 -1.4798 -3.4515 1.6194
0.1537 -0.1440 1.0096 -3.1071 -0.1535 0.7281 1.1808 -0.8466 1.6194 0.4343
];
Hpert[7] = [
-0.7469 0.0912 0.8199 -2.7284 -1.5999 2.0026 -0.5828 2.6208 -0.8500 -0.9571
0.0912 -0.3571 0.5111 1.4264 -0.6965 1.1619 -0.2757 1.6020 1.5347 -1.1224
0.8199 0.5111 -2.1040 -1.3614 0.8454 -2.1223 -0.8729 0.6144 -1.0635 -2.5367
-2.7284 1.4264 -1.3614 2.5262 -0.4181 -1.2518 0.1317 2.7936 1.1168 -0.7344
-1.5999 -0.6965 0.8454 -0.4181 1.5106 0.6176 0.5513 1.5116 -2.3239 -0.6955
2.0026 1.1619 -2.1223 -1.2518 0.6176 5.4633 1.6022 -0.3483 0.8633 -0.9902
-0.5828 -0.2757 -0.8729 0.1317 0.5513 1.6022 1.5424 -4.2988 -1.3485 1.1396
2.6208 1.6020 0.6144 2.7936 1.5116 -0.3483 -4.2988 -1.9808 -0.7574 -3.0000
-0.8500 1.5347 -1.0635 1.1168 -2.3239 0.8633 -1.3485 -0.7574 0.5876 0.3886
-0.9571 -1.1224 -2.5367 -0.7344 -0.6955 -0.9902 1.1396 -3.0000 0.3886 0.6869
];
Hpert[8] = [
1.5164 -1.0288 -0.6916 0.3759 1.6597 -3.0491 0.4837 0.1155 -1.1908 0.9576
-1.0288 1.9415 -0.7931 -0.0116 -2.1883 -0.0430 0.6561 2.0801 0.0055 -1.6433
-0.6916 -0.7931 0.6634 -0.7923 1.8284 0.3040 2.3257 1.4869 1.1270 1.3369
0.3759 -0.0116 -0.7923 1.1778 -1.8739 0.8303 -1.4213 -0.9153 1.1512 0.4781
1.6597 -2.1883 1.8284 -1.8739 2.2191 -2.0111 0.7245 2.2823 1.7011 0.6088
-3.0491 -0.0430 0.3040 0.8303 -2.0111 1.1767 0.8441 -0.1872 0.3460 0.1573
0.4837 0.6561 2.3257 -1.4213 0.7245 0.8441 1.3245 -2.0105 0.7422 1.3061
0.1155 2.0801 1.4869 -0.9153 2.2823 -0.1872 -2.0105 -0.2994 -0.5946 -1.9085
-1.1908 0.0055 1.1270 1.1512 1.7011 0.3460 0.7422 -0.5946 0.5783 -0.3022
0.9576 -1.6433 1.3369 0.4781 0.6088 0.1573 1.3061 -1.9085 -0.3022 2.7907
];
Hpert[9] = [
0.8817 0.7863 -2.3402 1.2758 -3.0907 2.0810 -1.0098 -1.9281 -0.7349 1.3017
0.7863 -2.0121 -0.0244 -0.1908 -0.1163 1.7948 0.1342 0.2946 -0.7330 -0.2950
-2.3402 -0.0244 -1.4745 -0.1365 -1.2744 1.8877 1.1876 1.6389 -0.9335 -0.4737
1.2758 -0.1908 -0.1365 -2.1552 -0.1308 2.6412 -0.4795 0.1106 -0.2928 -0.9607
-3.0907 -0.1163 -1.2744 -0.1308 -1.3662 0.0490 -0.1207 -3.3537 -2.0114 -0.2681
2.0810 1.7948 1.8877 2.6412 0.0490 0.1392 -1.2287 -0.7792 -0.4053 -0.1721
-1.0098 0.1342 1.1876 -0.4795 -0.1207 -1.2287 3.0700 -0.4987 0.1676 -0.7327
-1.9281 0.2946 1.6389 0.1106 -3.3537 -0.7792 -0.4987 -3.1128 -0.4981 -2.1836
-0.7349 -0.7330 -0.9335 -0.2928 -2.0114 -0.4053 0.1676 -0.4981 -0.6024 0.0982
1.3017 -0.2950 -0.4737 -0.9607 -0.2681 -0.1721 -0.7327 -2.1836 0.0982 0.6548
];
Hpert[10] = [
1.4319 1.2969 -2.2161 -2.2473 1.4910 1.1407 0.1057 -0.2886 -1.4843 -0.9251
1.2969 1.9139 -0.2176 -0.3275 -0.2272 2.2352 -2.2959 3.1775 -0.7976 -1.4588
-2.2161 -0.2176 2.6874 -3.1484 1.0178 1.8879 -3.0266 0.3680 -0.6852 -1.1662
-2.2473 -0.3275 -3.1484 -3.2626 -0.3822 -0.7716 -0.6207 0.1180 -0.6043 -1.3290
1.4910 -0.2272 1.0178 -0.3822 -1.8160 1.1944 -0.6355 2.4854 1.8676 0.7282
1.1407 2.2352 1.8879 -0.7716 1.1944 -0.3192 0.2048 -1.5255 1.7923 0.8973
0.1057 -2.2959 -3.0266 -0.6207 -0.6355 0.2048 3.1646 1.9705 2.3559 -0.2590
-0.2886 3.1775 0.3680 0.1180 2.4854 -1.5255 1.9705 2.7122 0.5588 -0.9730
-1.4843 -0.7976 -0.6852 -0.6043 1.8676 1.7923 2.3559 0.5588 -4.3551 0.0627
-0.9251 -1.4588 -1.1662 -1.3290 0.7282 0.8973 -0.2590 -0.9730 0.0627 0.4352
];
Hpert[11] = [
3.3686 -0.2267 0.3990 2.5193 -0.0834 0.4644 0.8532 -0.6513 -3.3348 -3.7140
-0.2267 -1.2219 -1.7066 -2.5655 0.0363 -1.3587 -0.2413 2.2271 -1.3337 -0.0091
0.3990 -1.7066 2.4665 2.3814 0.1569 -1.7990 -0.0206 -2.1901 0.5169 4.0659
2.5193 -2.5655 2.3814 -0.5668 1.7352 -0.5087 1.6270 0.5661 -1.4503 -0.9417
-0.0834 0.0363 0.1569 1.7352 -1.5931 -3.1355 -1.3405 -0.7754 -2.5817 1.5303
0.4644 -1.3587 -1.7990 -0.5087 -3.1355 -2.7151 -2.5397 1.1861 -0.3338 2.4069
0.8532 -0.2413 -0.0206 1.6270 -1.3405 -2.5397 -1.3272 2.1564 -1.3315 -1.0731
-0.6513 2.2271 -2.1901 0.5661 -0.7754 1.1861 2.1564 -0.1457 0.0147 0.7800
-3.3348 -1.3337 0.5169 -1.4503 -2.5817 -0.3338 -1.3315 0.0147 -1.2993 0.7516
-3.7140 -0.0091 4.0659 -0.9417 1.5303 2.4069 -1.0731 0.7800 0.7516 0.0331
];
Hpert[12] = [
-0.1456 -1.8617 -1.0432 -1.0750 1.1634 0.4894 0.8040 -2.2214 -0.7694 -0.4022
-1.8617 -0.9485 0.0544 2.5685 0.3394 0.0892 -0.3911 -3.1052 -0.3992 2.8154
-1.0432 0.0544 0.3591 0.9051 0.4368 4.7687 0.5422 -1.4317 -0.2065 -0.0473
-1.0750 2.5685 0.9051 -0.3875 0.3219 -1.0467 -0.8930 -0.9560 -1.2953 -0.0049
1.1634 0.3394 0.4368 0.3219 0.8538 1.8843 1.0402 0.1995 -0.9157 1.7703
0.4894 0.0892 4.7687 -1.0467 1.8843 -3.9336 -0.1170 -1.8965 -0.9522 -0.8874
0.8040 -0.3911 0.5422 -0.8930 1.0402 -0.1170 -1.1216 0.1993 -2.5093 0.3517
-2.2214 -3.1052 -1.4317 -0.9560 0.1995 -1.8965 0.1993 -1.1169 1.4366 -0.4060
-0.7694 -0.3992 -0.2065 -1.2953 -0.9157 -0.9522 -2.5093 1.4366 -3.0959 0.0350
-0.4022 2.8154 -0.0473 -0.0049 1.7703 -0.8874 0.3517 -0.4060 0.0350 -1.3153
];
Hpert[13] = [
-1.5185 -1.3608 1.5537 0.7003 -2.1594 2.4307 0.1517 -1.5616 -0.3301 1.8532
-1.3608 -0.2127 1.1507 0.4849 -3.4171 -1.0890 -0.4338 0.4424 3.7614 1.4820
1.5537 1.1507 -0.2856 0.1298 0.7675 -0.6154 1.9924 0.3818 -0.5881 1.2259
0.7003 0.4849 0.1298 0.7106 0.7546 1.5283 0.3976 -0.9764 -2.1904 0.9571
-2.1594 -3.4171 0.7675 0.7546 1.2928 -2.4822 0.8102 1.3795 1.6737 1.3945
2.4307 -1.0890 -0.6154 1.5283 -2.4822 0.9140 2.1517 2.6613 -0.8490 1.4860
0.1517 -0.4338 1.9924 0.3976 0.8102 2.1517 0.1775 3.4246 -1.7911 1.1764
-1.5616 0.4424 0.3818 -0.9764 1.3795 2.6613 3.4246 -3.3497 -3.5146 0.8021
-0.3301 3.7614 -0.5881 -2.1904 1.6737 -0.8490 -1.7911 -3.5146 2.3497 1.1687
1.8532 1.4820 1.2259 0.9571 1.3945 1.4860 1.1764 0.8021 1.1687 -1.5614
];
Hpert[14] = [
1.0620 3.5062 1.1616 0.8691 0.4853 0.0522 -1.0879 -0.5845 1.0701 -0.3467
3.5062 0.4912 -0.9086 -0.0199 -0.0785 -0.5907 -0.9312 0.0560 3.0544 0.0370
1.1616 -0.9086 2.5890 -0.3884 0.8463 1.6362 -1.1092 0.8460 -0.7591 -1.3382
0.8691 -0.0199 -0.3884 0.1682 -0.2810 -2.1212 2.4718 -0.7551 0.2173 1.8061
0.4853 -0.0785 0.8463 -0.2810 5.1615 0.3964 -0.4144 0.9269 -0.4351 0.0425
0.0522 -0.5907 1.6362 -2.1212 0.3964 -0.9380 -1.4396 1.8829 0.8466 -0.5979
-1.0879 -0.9312 -1.1092 2.4718 -0.4144 -1.4396 -0.1494 -0.6958 0.4715 -1.0116
-0.5845 0.0560 0.8460 -0.7551 0.9269 1.8829 -0.6958 3.1006 2.0333 -0.8926
1.0701 3.0544 -0.7591 0.2173 -0.4351 0.8466 0.4715 2.0333 3.4442 -0.0583
-0.3467 0.0370 -1.3382 1.8061 0.0425 -0.5979 -1.0116 -0.8926 -0.0583 -1.0135
];
Hpert[15] = [
-4.2075 -1.1611 2.0052 -0.7372 3.2426 -1.2741 0.3981 1.3734 2.8618 0.1256
-1.1611 2.4705 -1.9167 2.1766 1.9147 0.2245 2.3064 -0.2141 -0.9027 1.2694
2.0052 -1.9167 -1.5209 -3.7971 -1.2494 0.6345 0.0506 -0.6883 -3.0050 0.6130
-0.7372 2.1766 -3.7971 1.8079 0.2806 -2.2570 1.7228 2.1483 1.0915 -0.8857
3.2426 1.9147 -1.2494 0.2806 3.0341 2.2205 -0.2904 -0.7545 -0.0186 1.2435
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];