169:. Similar factors arise also in quantum field theories; however, these can have indefinite sign (especially in the case of Fermions) or even be complex-valued, which precludes their direct interpretation as probabilities. In these cases, one has to resort to a reweighting procedure (i.e., interpret the absolute value as probability and multiply the sign or phase to the observable) to get a strictly positive reference distribution suitable for Monte Carlo sampling. However, it is well known that, in specific parameter ranges of the model under consideration, the oscillatory nature of the weight function can lead to a bad
206:
22:
150:
configurations. In this sense, there is a trade-off: instead of dealing with one very complicated many-body problem, one faces the calculation of an infinite number of simple external-field problems.
475:
Baeurle, S.A. (2003a). "The stationary phase auxiliary field Monte Carlo method: a new strategy for reducing the sign problem of auxiliary field methodologies".
504:
Baer, R.; Head-Gordon, M.; Neuhauser, D. (1998). "Shifted-contour auxiliary field Monte Carlo for ab initio electronic structure: Straddling the sign problem".
405:
Baeurle, S.A.; Martonak, R.; Parrinello, M. (2002a). "A field-theoretical approach to simulation in the classical canonical and grand canonical ensemble".
436:
Baeurle, S.A. (2002). "Method of
Gaussian Equivalent Representation: A New Technique for Reducing the Sign Problem of Functional Integral Methods".
235:
130:
The distinctive ingredient of "auxiliary-field Monte Carlo" is the fact that the interactions are decoupled by means of the application of the
90:
62:
69:
561:
343:
Baeurle, S.A. (2004). "Grand canonical auxiliary field Monte Carlo: a new technique for simulating open systems at high density".
131:
32:
76:
277:
Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L. (1981). "Monte Carlo calculations of coupled boson-fermion systems. I".
157:: the large sum over auxiliary-field configurations is performed by sampling over the most important ones, with a certain
58:
257:
228:
170:
47:
586:
581:
83:
576:
122:(Blankenbecler 1981, Ceperley 1977) or classical problems (Baeurle 2004, Baeurle 2003, Baeurle 2002a).
218:
43:
310:
Ceperley, D.; Chester, G.V.; Kalos, M.H. (1977). "Monte Carlo simulation of a many-fermion study".
222:
214:
182:
39:
239:
178:
174:
513:
484:
445:
414:
383:
352:
321:
288:
153:
It is here, as in other related methods, that Monte Carlo enters the game in the guise of
8:
194:
162:
154:
517:
488:
449:
418:
387:
356:
325:
292:
115:
496:
395:
461:
312:
279:
143:
119:
521:
492:
453:
422:
391:
360:
329:
296:
166:
135:
457:
364:
147:
139:
570:
333:
300:
465:
374:
Baeurle, S.A. (2003). "Computation within the auxiliary field approach".
276:
158:
539:
426:
525:
165:, this probability is usually given by the (positive semi-definite)
21:
125:
404:
503:
309:
562:
Theory and
Computation of Advanced Materials and Sensors Group
544:
146:
to the calculation of a sum or integral over all possible
549:
181:
and can be alleviated with analytical and numerical
114:is a method that allows the calculation, by use of
568:
227:but its sources remain unclear because it lacks
126:Reweighting procedure and numerical sign problem
48:introducing citations to additional sources
185:procedures (Baeurle 2002, Baeurle 2003a).
258:Learn how and when to remove this message
474:
118:, of averages of operators in many-body
38:Relevant discussion may be found on the
435:
373:
342:
177:procedure. The problem is known as the
569:
134:, which permits the reformulation of
199:
15:
132:Hubbard–Stratonovich transformation
13:
533:
14:
598:
555:
142:representation. This reduces the
204:
31:relies largely or entirely on a
20:
138:in terms of a scalar auxiliary-
1:
497:10.1016/S0010-4655(03)00284-4
458:10.1103/PhysRevLett.89.080602
396:10.1016/S0021-9991(02)00036-0
270:
59:"Auxiliary-field Monte Carlo"
365:10.1016/j.comphy.2003.11.001
7:
506:Journal of Chemical Physics
188:
112:Auxiliary-field Monte Carlo
10:
603:
334:10.1103/PhysRevB.16.3081
301:10.1103/PhysRevD.24.2278
213:This article includes a
183:convergence acceleration
242:more precise citations.
171:statistical convergence
179:numerical sign problem
116:Monte Carlo techniques
175:numerical integration
477:Comput. Phys. Commun
345:Comput. Phys. Commun
44:improve this article
587:Quantum Monte Carlo
582:Monte Carlo methods
518:1998JChPh.109.6219B
489:2003CoPhC.154..111B
450:2002PhRvL..89h0602B
419:2002JChPh.117.3027B
388:2003JCoPh.184..540B
357:2004CoPhC.157..201B
326:1977PhRvB..16.3081C
293:1981PhRvD..24.2278B
195:Quantum Monte Carlo
163:statistical physics
155:importance sampling
215:list of references
120:quantum mechanical
577:Quantum mechanics
427:10.1063/1.1488587
313:Physical Review B
280:Physical Review D
268:
267:
260:
144:many-body problem
109:
108:
94:
594:
529:
526:10.1063/1.477300
500:
469:
430:
399:
368:
337:
304:
263:
256:
252:
249:
243:
238:this article by
229:inline citations
208:
207:
200:
167:Boltzmann factor
136:many-body theory
104:
101:
95:
93:
52:
24:
16:
602:
601:
597:
596:
595:
593:
592:
591:
567:
566:
558:
536:
534:Implementations
438:Phys. Rev. Lett
376:J. Comput. Phys
273:
264:
253:
247:
244:
233:
219:related reading
209:
205:
191:
161:. In classical
148:auxiliary-field
128:
105:
99:
96:
53:
51:
37:
25:
12:
11:
5:
600:
590:
589:
584:
579:
565:
564:
557:
556:External links
554:
553:
552:
547:
542:
535:
532:
531:
530:
501:
483:(2): 111–120.
471:
470:
432:
431:
401:
400:
382:(2): 540–558.
370:
369:
351:(3): 201–206.
339:
338:
306:
305:
272:
269:
266:
265:
223:external links
212:
210:
203:
198:
197:
190:
187:
127:
124:
107:
106:
100:September 2010
42:. Please help
28:
26:
19:
9:
6:
4:
3:
2:
599:
588:
585:
583:
580:
578:
575:
574:
572:
563:
560:
559:
551:
548:
546:
543:
541:
538:
537:
527:
523:
519:
515:
511:
507:
502:
498:
494:
490:
486:
482:
478:
473:
472:
467:
463:
459:
455:
451:
447:
444:(8): 080602.
443:
439:
434:
433:
428:
424:
420:
416:
412:
408:
407:J. Chem. Phys
403:
402:
397:
393:
389:
385:
381:
377:
372:
371:
366:
362:
358:
354:
350:
346:
341:
340:
335:
331:
327:
323:
319:
315:
314:
308:
307:
302:
298:
294:
290:
286:
282:
281:
275:
274:
262:
259:
251:
248:November 2010
241:
237:
231:
230:
224:
220:
216:
211:
202:
201:
196:
193:
192:
186:
184:
180:
176:
172:
168:
164:
160:
156:
151:
149:
145:
141:
137:
133:
123:
121:
117:
113:
103:
92:
89:
85:
82:
78:
75:
71:
68:
64:
61: –
60:
56:
55:Find sources:
49:
45:
41:
35:
34:
33:single source
29:This article
27:
23:
18:
17:
512:(15): 6219.
509:
505:
480:
476:
441:
437:
410:
406:
379:
375:
348:
344:
317:
311:
284:
278:
254:
245:
234:Please help
226:
152:
129:
111:
110:
97:
87:
80:
73:
66:
54:
30:
413:(7): 3027.
320:(7): 3081.
287:(8): 2278.
240:introducing
159:probability
571:Categories
271:References
70:newspapers
40:talk page
466:12190451
189:See also
550:QMCPACK
514:Bibcode
485:Bibcode
446:Bibcode
415:Bibcode
384:Bibcode
353:Bibcode
322:Bibcode
289:Bibcode
236:improve
173:of the
84:scholar
464:
86:
79:
72:
65:
57:
545:QUEST
221:, or
140:field
91:JSTOR
77:books
462:PMID
63:news
540:ALF
522:doi
510:109
493:doi
481:154
454:doi
423:doi
411:117
392:doi
380:184
361:doi
349:157
330:doi
297:doi
46:by
573::
520:.
508:.
491:.
479:.
460:.
452:.
442:89
440:.
421:.
409:.
390:.
378:.
359:.
347:.
328:.
318:16
316:.
295:.
285:24
283:.
225:,
217:,
528:.
524::
516::
499:.
495::
487::
468:.
456::
448::
429:.
425::
417::
398:.
394::
386::
367:.
363::
355::
336:.
332::
324::
303:.
299::
291::
261:)
255:(
250:)
246:(
232:.
102:)
98:(
88:·
81:·
74:·
67:·
50:.
36:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.