I want to write a DMRG code for Majumdar-Ghosh model but defined on a spin chain with odd site, and PBC.
The Hamiltonian is defined as:
os = OpSum()
for j = 1:N-1
os += 0.5, “S+”, j, “S-”, j + 1
os += 0.5, “S-”, j, “S+”, j + 1
os += 1.0, “Sz”, j, “Sz”, j + 1
end
for j = 1:N-2
os += 0.25, “S+”, j, “S-”, j + 2
os += 0.25, “S-”, j, “S+”, j + 2
os += 0.5, “Sz”, j, “Sz”, j + 2
end
os += 0.5, “S+”, 1, “S-”, N
os += 0.5, “S-”, 1, “S+”, N
os += 1.0, “Sz”, 1, “Sz”, N
os += 0.25, “S+”, 1, “S-”, N-1
os += 0.25, “S-”, 1, “S+”, N-1
os += 0.5, “Sz”, 1, “Sz”, N-1
os += 0.25, “S+”, 2, “S-”, N
os += 0.25, “S-”, 2, “S+”, N
os += 0.5, “Sz”, 2, “Sz”, N
where N is defined as 2M-1 (like 127, 111, 95, 79, 63…)
When I run the code, I found the output like
After sweep 1 energy=-44.481929186344885 maxlinkdim=300 maxerr=8.69E-04 time=86.664
After sweep 2 energy=-44.491945171337946 maxlinkdim=294 maxerr=1.82E-11 time=56.699
After sweep 3 energy=-44.49596888252315 maxlinkdim=300 maxerr=2.79E-11 time=28.780
After sweep 4 energy=-44.49831553410645 maxlinkdim=284 maxerr=1.00E-12 time=14.488
After sweep 5 energy=-44.499941228459406 maxlinkdim=241 maxerr=9.99E-13 time=9.099
After sweep 6 energy=-44.50115479519257 maxlinkdim=236 maxerr=9.98E-13 time=7.928
After sweep 7 energy=-44.5020439307327 maxlinkdim=230 maxerr=9.98E-13 time=7.746
After sweep 8 energy=-44.50274876800401 maxlinkdim=209 maxerr=9.98E-13 time=6.959
After sweep 9 energy=-44.50339952131439 maxlinkdim=185 maxerr=9.99E-13 time=5.806
After sweep 10 energy=-44.503907791478824 maxlinkdim=162 maxerr=9.98E-13 time=3.995
After sweep 11 energy=-44.50434542303579 maxlinkdim=141 maxerr=9.98E-13 time=3.305
After sweep 12 energy=-44.50467922723091 maxlinkdim=123 maxerr=9.99E-13 time=2.544
After sweep 13 energy=-44.50494644606336 maxlinkdim=107 maxerr=9.99E-13 time=2.186
After sweep 14 energy=-44.50515744754459 maxlinkdim=88 maxerr=9.95E-13 time=1.659
After sweep 15 energy=-44.50533817095654 maxlinkdim=80 maxerr=9.96E-13 time=1.653
After sweep 16 energy=-44.50552529916788 maxlinkdim=78 maxerr=9.99E-13 time=1.350
After sweep 17 energy=-44.50571174377446 maxlinkdim=78 maxerr=1.00E-12 time=1.562
After sweep 18 energy=-44.505886707568344 maxlinkdim=73 maxerr=1.00E-12 time=1.279
After sweep 19 energy=-44.506031127699295 maxlinkdim=72 maxerr=9.99E-13 time=1.573
After sweep 20 energy=-44.50614257554192 maxlinkdim=63 maxerr=9.96E-13 time=1.247
After sweep 21 energy=-44.50622600499852 maxlinkdim=55 maxerr=9.99E-13 time=1.146
After sweep 22 energy=-44.506308740273 maxlinkdim=51 maxerr=9.96E-13 time=1.310
After sweep 23 energy=-44.50639583445144 maxlinkdim=49 maxerr=1.00E-12 time=0.968
After sweep 24 energy=-44.50649899547017 maxlinkdim=66 maxerr=9.98E-13 time=1.274
After sweep 25 energy=-44.50658135710624 maxlinkdim=53 maxerr=1.00E-12 time=1.377
After sweep 26 energy=-44.50663860455781 maxlinkdim=50 maxerr=1.00E-12 time=1.112
After sweep 27 energy=-44.50669707260257 maxlinkdim=63 maxerr=9.99E-13 time=1.397
After sweep 28 energy=-44.50674986889638 maxlinkdim=56 maxerr=9.98E-13 time=1.157
After sweep 29 energy=-44.506795094424106 maxlinkdim=49 maxerr=9.94E-13 time=1.054
After sweep 30 energy=-44.506842287314576 maxlinkdim=47 maxerr=9.99E-13 time=1.403
After sweep 31 energy=-44.5069124670681 maxlinkdim=59 maxerr=9.99E-13 time=1.094
After sweep 32 energy=-44.506966178281175 maxlinkdim=53 maxerr=1.00E-12 time=1.264
After sweep 33 energy=-44.50701140060947 maxlinkdim=48 maxerr=9.97E-13 time=1.459
After sweep 34 energy=-44.50705438963784 maxlinkdim=49 maxerr=9.96E-13 time=1.450
After sweep 35 energy=-44.50709172757356 maxlinkdim=44 maxerr=9.99E-13 time=1.481
After sweep 36 energy=-44.50712029911698 maxlinkdim=44 maxerr=9.99E-13 time=1.250
After sweep 37 energy=-44.50714873624605 maxlinkdim=45 maxerr=1.00E-12 time=1.281
After sweep 38 energy=-44.50717753916703 maxlinkdim=50 maxerr=9.95E-13 time=1.443
After sweep 39 energy=-44.50720567342386 maxlinkdim=51 maxerr=9.98E-13 time=1.254
After sweep 40 energy=-44.50723066557673 maxlinkdim=46 maxerr=9.97E-13 time=1.275
After sweep 41 energy=-44.507255748411374 maxlinkdim=46 maxerr=9.99E-13 time=1.523
After sweep 42 energy=-44.50727752728447 maxlinkdim=46 maxerr=9.99E-13 time=1.301
After sweep 43 energy=-44.50729802345977 maxlinkdim=51 maxerr=9.99E-13 time=1.601
After sweep 44 energy=-44.50731794456762 maxlinkdim=51 maxerr=9.99E-13 time=1.299
After sweep 45 energy=-44.50733591769872 maxlinkdim=57 maxerr=1.00E-12 time=1.603
After sweep 46 energy=-44.50735128040145 maxlinkdim=51 maxerr=9.98E-13 time=1.212
After sweep 47 energy=-44.50736700247448 maxlinkdim=57 maxerr=1.00E-12 time=1.401
After sweep 48 energy=-44.50737990968225 maxlinkdim=45 maxerr=1.00E-12 time=1.612
After sweep 49 energy=-44.50739000230962 maxlinkdim=46 maxerr=9.97E-13 time=1.343
After sweep 50 energy=-44.507399622370265 maxlinkdim=43 maxerr=9.98E-13 time=1.553
After sweep 51 energy=-44.50740816650574 maxlinkdim=45 maxerr=9.99E-13 time=1.210
After sweep 52 energy=-44.50741592984533 maxlinkdim=47 maxerr=1.00E-12 time=1.373
After sweep 53 energy=-44.507423293004976 maxlinkdim=48 maxerr=9.99E-13 time=1.529
After sweep 54 energy=-44.50742982522328 maxlinkdim=51 maxerr=1.00E-12 time=1.234
After sweep 55 energy=-44.50743583743276 maxlinkdim=50 maxerr=9.98E-13 time=1.556
After sweep 56 energy=-44.50744143999142 maxlinkdim=53 maxerr=9.96E-13 time=1.299
After sweep 57 energy=-44.5074461689624 maxlinkdim=56 maxerr=9.99E-13 time=1.610
After sweep 58 energy=-44.507450464650695 maxlinkdim=51 maxerr=9.97E-13 time=1.348
After sweep 59 energy=-44.507454019576734 maxlinkdim=45 maxerr=1.00E-12 time=1.273
After sweep 60 energy=-44.50745718651609 maxlinkdim=49 maxerr=9.96E-13 time=1.540
After sweep 61 energy=-44.50746002541054 maxlinkdim=48 maxerr=9.99E-13 time=1.302
After sweep 62 energy=-44.50746268734314 maxlinkdim=50 maxerr=9.99E-13 time=1.617
After sweep 63 energy=-44.50746485884627 maxlinkdim=48 maxerr=9.96E-13 time=1.328
After sweep 64 energy=-44.50746670663664 maxlinkdim=48 maxerr=9.99E-13 time=1.276
After sweep 65 energy=-44.507468421502004 maxlinkdim=53 maxerr=1.00E-12 time=1.558
After sweep 66 energy=-44.50746989879488 maxlinkdim=50 maxerr=1.00E-12 time=1.309
After sweep 67 energy=-44.50747118044341 maxlinkdim=52 maxerr=1.00E-12 time=1.586
After sweep 68 energy=-44.50747232598204 maxlinkdim=55 maxerr=1.00E-12 time=1.390
After sweep 69 energy=-44.507473324056576 maxlinkdim=55 maxerr=1.00E-12 time=1.367
After sweep 70 energy=-44.50747413739557 maxlinkdim=56 maxerr=1.00E-12 time=1.557
After sweep 71 energy=-44.50747482576718 maxlinkdim=49 maxerr=9.95E-13 time=1.274
After sweep 72 energy=-44.50747540547035 maxlinkdim=46 maxerr=9.99E-13 time=1.571
After sweep 73 energy=-44.50747588201757 maxlinkdim=48 maxerr=1.00E-12 time=1.374
After sweep 74 energy=-44.50747630807204 maxlinkdim=48 maxerr=9.98E-13 time=1.575
After sweep 75 energy=-44.50747666458328 maxlinkdim=47 maxerr=9.98E-13 time=1.277
After sweep 76 energy=-44.50747698781786 maxlinkdim=49 maxerr=9.98E-13 time=1.284
After sweep 77 energy=-44.507477280049905 maxlinkdim=51 maxerr=9.99E-13 time=1.574
After sweep 78 energy=-44.50747753506067 maxlinkdim=47 maxerr=1.00E-12 time=1.359
After sweep 79 energy=-44.50747774828389 maxlinkdim=48 maxerr=9.99E-13 time=1.564
After sweep 80 energy=-44.507477937831155 maxlinkdim=48 maxerr=1.00E-12 time=1.323
After sweep 81 energy=-44.507478095157616 maxlinkdim=46 maxerr=9.99E-13 time=1.336
After sweep 82 energy=-44.5074782382683 maxlinkdim=49 maxerr=9.98E-13 time=1.618
After sweep 83 energy=-44.50747836658586 maxlinkdim=47 maxerr=9.99E-13 time=1.283
After sweep 84 energy=-44.50747848408119 maxlinkdim=48 maxerr=1.00E-12 time=1.554
After sweep 85 energy=-44.50747858622078 maxlinkdim=48 maxerr=9.97E-13 time=1.318
After sweep 86 energy=-44.50747867474391 maxlinkdim=53 maxerr=9.99E-13 time=1.614
After sweep 87 energy=-44.507478752107005 maxlinkdim=52 maxerr=1.00E-12 time=1.325
After sweep 88 energy=-44.507478821271526 maxlinkdim=50 maxerr=1.00E-12 time=1.358
After sweep 89 energy=-44.50747888444592 maxlinkdim=50 maxerr=9.98E-13 time=1.426
After sweep 90 energy=-44.50747893956039 maxlinkdim=52 maxerr=9.98E-13 time=1.298
After sweep 91 energy=-44.50747898836787 maxlinkdim=56 maxerr=9.98E-13 time=1.590
After sweep 92 energy=-44.507479031383994 maxlinkdim=54 maxerr=9.99E-13 time=1.339
After sweep 93 energy=-44.50747907004947 maxlinkdim=50 maxerr=9.98E-13 time=1.314
After sweep 94 energy=-44.50747910655964 maxlinkdim=51 maxerr=1.00E-12 time=1.508
After sweep 95 energy=-44.50747913518592 maxlinkdim=52 maxerr=1.00E-12 time=1.247
After sweep 96 energy=-44.507479161232645 maxlinkdim=48 maxerr=1.00E-12 time=1.656
After sweep 97 energy=-44.50747918253786 maxlinkdim=52 maxerr=1.00E-12 time=1.369
After sweep 98 energy=-44.507479198563665 maxlinkdim=46 maxerr=9.98E-13 time=1.331
After sweep 99 energy=-44.50747921066809 maxlinkdim=44 maxerr=9.98E-13 time=1.542
After sweep 100 energy=-44.50747921997647 maxlinkdim=43 maxerr=9.92E-13 time=1.246
It seems so weird… Could I believe that it is converged? Here, I guess the system is gapless, so are there any other possible way to improve this?
Thanks