Please wait a minute...
Chin. Phys. B, 2018, Vol. 27(8): 087501    DOI: 10.1088/1674-1056/27/8/087501
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Typicality at quantum-critical points

Lu Liu(刘录)1, Anders W Sandvik2,3, Wenan Guo(郭文安)1
1 Department of Physics, Beijing Normal University, Beijing 100875, China;
2 Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA;
3 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
Abstract  

We discuss the concept of typicality of quantum states at quantum-critical points, using projector Monte Carlo simulations of an S=1/2 bilayer Heisenberg antiferromagnet as an illustration. With the projection (imaginary) time τ scaled as τ=aLz, L being the system length and z the dynamic critical exponent (which takes the value z=1 in the bilayer model studied here), a critical point can be identified which asymptotically flows to the correct location and universality class with increasing L, independently of the prefactor a and the initial state. Varying the proportionality factor a and the initial state only changes the cross-over behavior into the asymptotic large-L behavior. In some cases, choosing an optimal factor a may also lead to the vanishing of the leading finite-size corrections. The observation of typicality can be used to speed up simulations of quantum criticality, not only within the Monte Carlo approach but also with other numerical methods where imaginary-time evolution is employed, e.g., tensor network states, as it is not necessary to evolve fully to the ground state but only for sufficiently long times to reach the typicality regime.

Keywords:  typicality      quantum criticality      bilayer Heisenberg antiferromagnet model      imaginary projecting time      projecting quantum Monte Carlo simulation  
Received:  11 May 2018      Revised:  19 May 2018      Accepted manuscript online: 
PACS:  75.10.Kt (Quantum spin liquids, valence bond phases and related phenomena)  
  75.10.Jm (Quantized spin models, including quantum spin frustration)  
  75.40.Mg (Numerical simulation studies)  
  75.40.-s (Critical-point effects, specific heats, short-range order)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos. 11734002 and 11775021), the National Science Foundation (Grant No. DMR-1710170), and a Simons Investigator Award.

Corresponding Authors:  Anders W Sandvik, Wenan Guo     E-mail:  sandvik@bu.edu;waguo@bnu.edu.cn

Cite this article: 

Lu Liu(刘录), Anders W Sandvik, Wenan Guo(郭文安) Typicality at quantum-critical points 2018 Chin. Phys. B 27 087501

[1] von Neumann J 1929 Z. Phys. 57 30 (English translation) 2010 Eur. Phys. J. H 35 201
[2] Goldstein S, Lebowitz J L, Tumulka R and Zanghi N 2006 Phys. Rev. Lett. 96 050403
[3] Goldstein S, Lebowitz J L, Tumulka R and Zanghi N 2010 Eur. Phys. J. H 35 173
[4] Srednicki M 1994 Phys. Rev. E 50 888
[5] Sugiura S and Shimizu A 2012 Phys. Rev. Lett. 108 240401
[6] Sugiura S and Shimizu A 2013 Phys. Rev. Lett. 111 010401
[7] Deutsch J M 1991 Phys. Rev. A 43 2046
[8] Rigol M and Srednicki M 2012 Phys. Rev. Lett. 108 110601
[9] Jaklič J and Prelovšek P 1994 Phys. Rev. B 49 5065
[10] Jaklič J and Prelovšek P 2000 Adv. Phys. 49 1
[11] White S R 2009 Phys. Rev. Lett. 102 190601
[12] Garnerone S, de Oliveira T R and Zanardi P 2010 Phys. Rev. A 81 032336
[13] Liang S 1990 Phys. Rev. B 42 6555
[14] Sandvik A W 2005 Phys. Rev. Lett. 95 207203
[15] Sandvik A W and Kurkijärvi J 1991 Phys. Rev. B 43 5950
[16] Sandvik A W 2010 AIP Conf. Proc. 1297 135
[17] Wang L and Sandvik A W 2010 Phys. Rev. B 81 054417
[18] Shu Y R, Yin S and Yao D X 2017 Phys. Rev. B 96 094304
[19] Hida K 1990 J. Phys. Soc. Jpn. 59 2230
[20] Hida K 1992 J. Phys. Soc. Jpn. 61 1013
[21] Millis A J and Monien H 1993 Phys. Rev. Lett. 70 2810
[22] Sandvik A W and Scalapino D J 1994 Phys. Rev. Lett. 72 2777
[23] Manousakis E 1991 Rev. Mod. Phys. 63 1
[24] Chakravarty S, Halperin B I and Nelson D R 1988 Phys. Rev. Lett. 60 1057
[25] Chubukov A V, Sachdev S and Ye J 1994 Phys. Rev. B 49 11919
[26] Sachdev S 2011 Quantum Phase Transitions, 2nd edn. (Cambridge: Cambridge University Press)
[27] Wang L, Beach K S D and Sandvik A W 2006 Phys. Rev. B 73 014431
[28] Campostrini M, Hasenbusch M, Pelissetto A, Rossi P and Vicari E 2002 Phys. Rev. B 65 144520
[29] Matsumoto M, Yasuda C, Todo S and Takayama H 2001 Phys. Rev. B 65 014407
[30] Wenzel S, Bogacz L and Janke W 2008 Phys. Rev. Lett. 101 127202
[31] Jiang F J 2012 Phys. Rev. B 85 014414
[32] Fritz L, Doretto R L, Wessel S, Wenzel S, Burdin S and Vojta M 2011 Phys. Rev. B 83 174416
[33] Ma N, Weinberg P, Shao H, Guo W, Yao D X and Sandvik A W arXiv: 1804.01273
[34] Liang S, Doucot B and Anderson P W 1988 Phys. Rev. Lett. 61 365
[35] Sandvik A W and Evertz H G 2010 Phys. Rev. B 82 024407
[36] Lou J and Sandvik A W 2007 Phys. Rev. B 76 104432
[37] Lin Y C, Tang Y, Lou J and Sandvik A W 2012 Phys. Rev. B 86 144405
[38] Carleo G and Troyer M 2017 Science 355 602
[39] Beach K S D and Sandvik A W 2006 Nucl. Phys. B 750 142
[40] Binder K 1981 Phys. Rev. Lett. 47 693
[41] Binder K 1981 Z. Phys. B: Condens. Matter 43 119
[42] Pollock E L and Ceperley D M 1987 Phys. Rev. B 36 8343
[43] Barber M N 1983 in Phase Transitions and Critical Phenaomena Vol. 8, eds. Domb C and Lebowitz J (London: Academic)
[44] Luck J M 1985 Phys. Rev. B 31 3069
[45] Shao H, Guo W A and Sandvik A W 2016 Science 352 213
[46] Fisher M P A, Weichman P B, Grinstein G and Fisher D S 1989 Phys. Rev. B 40 546
[47] Kamieniarzand G and Blöte H W J 1993 J. Phys. A: Math. Gen. 26 201
[48] Yasuda S and Todo S 2013 Phys. Rev. E 88 061301
[1] Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
Bowen Zhao(赵博文), Jun Takahashi, Anders W. Sandvik. Chin. Phys. B, 2020, 29(5): 057506.
[2] Quantum critical duality in two-dimensional Dirac semimetals
Jiang Zhou(周江), Ya-Jie Wu(吴亚杰), Su-Peng Kou(寇谡鹏). Chin. Phys. B, 2019, 28(1): 017402.
No Suggested Reading articles found!