561:
99:
divided into blocks that gain energy if and only if they represent a full computation by a Turing machine, and showing that this system becomes gapped if and only if the machine does not halt.
602:
448:
95:
the machine halts. The one-dimensional case was also proven undecidable in 2020 by constructing a chain of interacting
221:
Nachtergaele, Bruno; Sims, Robert (22 March 2006). "Lieb-Robinson Bounds and the
Exponential Clustering Theorem".
44:
636:
631:
626:
134:
Cubitt, Toby S.; Perez-Garcia, David; Wolf, Michael M. (2015-12-10). "Undecidability of the spectral gap".
108:
76:
In quantum many-body systems, ground states of gapped
Hamiltonians have exponential decay of correlations.
274:
Hastings, Matthew B.; Koma, Tohru (22 April 2006). "Spectral Gap and
Exponential Decay of Correlations".
449:"Why Some Physicists Are Excited About the Undecidability of the Spectral Gap Problem and Why Should We"
621:
595:
480:
386:
Cubitt, Toby S.; Perez-Garcia, David; Wolf, Michael M. (2015). "Undecidability of the spectral gap".
576:
88:
588:
522:
405:
350:
293:
240:
153:
8:
80:
79:
In 2015, it was shown that the problem of determining the existence of a spectral gap is
62:
526:
499:
Bausch, Johannes; Cubitt, Toby S.; Lucia, Angelo; Perez-Garcia, David (17 August 2020).
409:
354:
297:
244:
157:
540:
512:
429:
395:
340:
309:
283:
256:
230:
177:
143:
48:
568:
421:
368:
169:
20:
544:
530:
433:
413:
363:
358:
328:
313:
301:
248:
181:
161:
84:
66:
260:
572:
535:
500:
92:
305:
252:
615:
32:
197:"Scientists Just Proved A Fundamental Quantum Physics Problem is Unsolvable"
425:
372:
173:
113:
28:
478:
Cubitt, Toby S.; Perez-Garcia, David; Wolf, Michael M. (November 2018).
417:
288:
235:
165:
69:
of electrons in a solid material, in which case it is often known as an
70:
453:
Bulletin of the
European Association for Theoretical Computer Science
517:
400:
345:
148:
36:
40:
560:
498:
196:
96:
329:"Correlation Length versus Gap in Frustration-Free Systems"
91:
and showed that this hypothetical material becomes gapped
16:
Energy difference between ground and first excited states
477:
385:
133:
501:"Undecidability of the Spectral Gap in One Dimension"
479:
27:of a system is the energy difference between its
613:
220:
83:in two or more dimensions. The authors used an
596:
327:Gosset, David; Huang, Yichen (3 March 2016).
65:, the most important spectral gap is for the
273:
326:
603:
589:
534:
516:
440:
399:
362:
344:
287:
234:
147:
614:
446:
276:Communications in Mathematical Physics
223:Communications in Mathematical Physics
555:
379:
194:
54:, and those that do not are called
13:
14:
648:
559:
47:with a spectral gap is called a
39:is the spectral gap between the
195:Lim, Jappy (11 December 2015).
492:
471:
364:10.1103/PhysRevLett.116.097202
320:
267:
214:
188:
127:
43:and the lightest particle. A
1:
120:
575:. You can help Knowledge by
109:List of undecidable problems
7:
102:
10:
653:
554:
536:10.1103/PhysRevX.10.031038
306:10.1007/s00220-006-0030-4
253:10.1007/s00220-006-1556-1
481:"The Unsolvable Problem"
333:Physical Review Letters
89:quantum Turing machines
571:-related article is a
637:Quantum physics stubs
142:(7581). US: 207–211.
632:Undecidable problems
447:Kreinovich, Vladik.
627:Physical quantities
527:2020PhRvX..10c1038B
486:Scientific American
418:10.1038/nature16059
410:2015Natur.528..207C
355:2016PhRvL.116i7202G
298:2006CMaPh.265..781H
245:2006CMaPh.265..119N
166:10.1038/nature16059
158:2015Natur.528..207C
63:solid-state physics
622:Quantum mechanics
584:
583:
569:quantum mechanics
505:Physical Review X
394:(7581): 207–211.
21:quantum mechanics
644:
605:
598:
591:
563:
556:
549:
548:
538:
520:
496:
490:
489:
483:
475:
469:
468:
466:
464:
444:
438:
437:
403:
383:
377:
376:
366:
348:
324:
318:
317:
291:
271:
265:
264:
238:
218:
212:
211:
209:
207:
192:
186:
185:
151:
131:
116:, in mathematics
85:aperiodic tiling
67:many-body system
652:
651:
647:
646:
645:
643:
642:
641:
612:
611:
610:
609:
553:
552:
497:
493:
476:
472:
462:
460:
445:
441:
384:
380:
325:
321:
289:math-ph/0507008
272:
268:
236:math-ph/0506030
219:
215:
205:
203:
193:
189:
132:
128:
123:
105:
17:
12:
11:
5:
650:
640:
639:
634:
629:
624:
608:
607:
600:
593:
585:
582:
581:
564:
551:
550:
491:
470:
439:
378:
319:
282:(3): 781–804.
266:
229:(1): 119–130.
213:
187:
125:
124:
122:
119:
118:
117:
111:
104:
101:
93:if and only if
31:and its first
15:
9:
6:
4:
3:
2:
649:
638:
635:
633:
630:
628:
625:
623:
620:
619:
617:
606:
601:
599:
594:
592:
587:
586:
580:
578:
574:
570:
565:
562:
558:
557:
546:
542:
537:
532:
528:
524:
519:
514:
511:(3): 031038.
510:
506:
502:
495:
487:
482:
474:
458:
454:
450:
443:
435:
431:
427:
423:
419:
415:
411:
407:
402:
397:
393:
389:
382:
374:
370:
365:
360:
356:
352:
347:
342:
339:(9): 097202.
338:
334:
330:
323:
315:
311:
307:
303:
299:
295:
290:
285:
281:
277:
270:
262:
258:
254:
250:
246:
242:
237:
232:
228:
224:
217:
202:
198:
191:
183:
179:
175:
171:
167:
163:
159:
155:
150:
145:
141:
137:
130:
126:
115:
112:
110:
107:
106:
100:
98:
94:
90:
86:
82:
77:
74:
72:
68:
64:
59:
57:
53:
51:
46:
42:
38:
34:
33:excited state
30:
26:
22:
577:expanding it
566:
508:
504:
494:
485:
473:
461:. Retrieved
456:
452:
442:
391:
387:
381:
336:
332:
322:
279:
275:
269:
226:
222:
216:
204:. Retrieved
200:
190:
139:
135:
129:
114:Spectral gap
78:
75:
60:
55:
49:
29:ground state
25:spectral gap
24:
18:
463:18 December
206:18 December
81:undecidable
52:Hamiltonian
45:Hamiltonian
616:Categories
518:1810.01858
401:1502.04135
346:1509.06360
149:1502.04135
121:References
71:energy gap
545:73583883
426:26659181
373:26991196
201:Futurism
174:26659181
103:See also
37:mass gap
523:Bibcode
434:4451987
406:Bibcode
351:Bibcode
314:7941730
294:Bibcode
241:Bibcode
182:4451987
154:Bibcode
56:gapless
543:
459:(2017)
432:
424:
388:Nature
371:
312:
261:815023
259:
180:
172:
136:Nature
97:qudits
50:gapped
41:vacuum
35:. The
23:, the
567:This
541:S2CID
513:arXiv
430:S2CID
396:arXiv
341:arXiv
310:S2CID
284:arXiv
257:S2CID
231:arXiv
178:S2CID
144:arXiv
573:stub
465:2018
422:PMID
369:PMID
208:2018
170:PMID
531:doi
457:122
414:doi
392:528
359:doi
337:116
302:doi
280:265
249:doi
227:265
162:doi
140:528
87:of
61:In
19:In
618::
539:.
529:.
521:.
509:10
507:.
503:.
484:.
455:.
451:.
428:.
420:.
412:.
404:.
390:.
367:.
357:.
349:.
335:.
331:.
308:.
300:.
292:.
278:.
255:.
247:.
239:.
225:.
199:.
176:.
168:.
160:.
152:.
138:.
73:.
58:.
604:e
597:t
590:v
579:.
547:.
533::
525::
515::
488:.
467:.
436:.
416::
408::
398::
375:.
361::
353::
343::
316:.
304::
296::
286::
263:.
251::
243::
233::
210:.
184:.
164::
156::
146::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.