Chin. Phys. Lett.  2020, Vol. 37 Issue (5): 057502    DOI: 10.1088/0256-307X/37/5/057502
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
Consistent Scaling Exponents at the Deconfined Quantum-Critical Point
Anders W. Sandvik1,2**, Bowen Zhao1
1Department of Physics, Boston University, Boston, Massachusetts 02215, USA
2Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190
Cite this article:   
Anders W. Sandvik, Bowen Zhao 2020 Chin. Phys. Lett. 37 057502
Download: PDF(686KB)   PDF(mobile)(679KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract We report a quantum Monte Carlo study of the phase transition between antiferromagnetic and valence-bond solid ground states in the square-lattice $S=1/2$ $J$–$Q$ model. The critical correlation function of the $Q$ terms gives a scaling dimension corresponding to the value $\nu = 0.455 \pm 0.002$ of the correlation-length exponent. This value agrees with previous (less precise) results from conventional methods, e.g., finite-size scaling of the near-critical order parameters. We also study the $Q$-derivatives of the Binder cumulants of the order parameters for $L^2$ lattices with $L$ up to $448$. The slope grows as $L^{1/\nu}$ with a value of $\nu$ consistent with the scaling dimension of the $Q$ term. There are no indications of runaway flow to a first-order phase transition. The mutually consistent estimates of $\nu$ provide compelling support for a continuous deconfined quantum-critical point.
Received: 06 April 2020      Published: 21 April 2020
PACS:  75.10.Jm (Quantized spin models, including quantum spin frustration)  
  64.70.Tg (Quantum phase transitions)  
  75.40.Mg (Numerical simulation studies)  
  75.30.Kz (Magnetic phase boundaries (including classical and quantum magnetic transitions, metamagnetism, etc.))  
Fund: Supported by the National Science Foundation (USA) under Grant No. DMR-1710170 and by the Simons Foundation under a Simons Investigator Award.
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/37/5/057502       OR      https://cpl.iphy.ac.cn/Y2020/V37/I5/057502
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Anders W. Sandvik
Bowen Zhao
[1]Sachdev S 2008 Nat. Phys. 4 173
[2]Savary L and Balents L 2017 Rep. Prog. Phys. 80 016502
[3]Wen X G 2019 Science 363 eaal3099
[4]Senthil T, Vishwanath A, Balents L, Sachdev S and Fisher M P A 2004 Science 303 1490
[5]Kaul R K, Melko R G and Sandvik A W 2013 Annu. Rev. Condens. Matter Phys. 4 179
[6]Sandvik A W, Daul S, Singh R R P and Scalapino D J 2002 Phys. Rev. Lett. 89 247201
[7]Haldane F D M 1988 Phys. Rev. Lett. 61 1029
[8]Chakravarty S, Halperin B I and Nelson D R 1989 Phys. Rev. B 39 2344
[9]Read N and Sachdev S 1989 Phys. Rev. Lett. 62 1694
[10]Read N and Sachdev S 1990 Phys. Rev. B 42 4568
[11]Dagotto E and Moreo A 1989 Phys. Rev. Lett. 63 2148
[12]Murthy G and Sachdev S 1990 Nucl. Phys. B 344 557
[13]Motrunich O I and Vishwanath A 2004 Phys. Rev. B 70 075104
[14]Sandvik A W 2007 Phys. Rev. Lett. 98 227202
[15]Melko R G and Kaul R K 2008 Phys. Rev. Lett. 100 017203
[16]Jiang F J, Nyfeler M, Chandrasekharan S and Wiese U J 2008 J. Stat. Mech.: Theory Exp. 2008 P02009
[17]Lou J, Sandvik A W and Kawashima N 2009 Phys. Rev. B 80 180414
[18]Sandvik A W 2010 Phys. Rev. Lett. 104 177201
[19]Kaul R K 2011 Phys. Rev. B 84 054407
[20]Sandvik A W 2012 Phys. Rev. B 85 134407
[21]Harada K, Suzuki T, Okubo T, Matsuo H, Lou J, Watanabe H, Todo S and Kawashima N 2013 Phys. Rev. B 88 220408
[22]Chen K, Huang Y, Deng Y, Kuklov A B, Prokof'ev N V and Svistunov B V 2013 Phys. Rev. Lett. 110 185701
[23]Block M S, Melko R G and Kaul R K 2013 Phys. Rev. Lett. 111 137202
[24]Pujari S, Alet F and Damle K 2015 Phys. Rev. B 91 104411
[25]Suwa H, Sen A and Sandvik A W 2016 Phys. Rev. B 94 144416
[26]Shao H, Guo W and Sandvik A W 2016 Science 352 213
[27]Ma N, Sun G Y, You Y Z, Xu C, Vishwanath A, Sandvik A W and Meng Z Y 2018 Phys. Rev. B 98 174421
[28]Evertz H G 2003 Adv. Phys. 52 1
[29]Sandvik A W 1999 Phys. Rev. B 59 R14157
[30]Sandvik A W 2010 AIP Conf. Proc. 1297 135
[31]Nahum A, Serna P, Chalker J T, Ortuño M and Somoza A M 2015 Phys. Rev. Lett. 115 267203
[32]Nahum A, Chalker J T, Serna P, Ortuño M and Somoza A M 2015 Phys. Rev. X 5 041048
[33]Zhao B, Weinberg P and Sandvik A W 2019 Nat. Phys. 15 678
[34]Serna P and Nahum A 2019 Phys. Rev. B 99 195110
[35]Takahashi J and Sandvik A W 2020 arXiv:2001.10045
[36]Kuklov A B, Matsumoto M, Prokof’ev N V, Svistunov B V, Troyer M 2008 Phys. Rev. Lett. 101 050405
[37]Levin M and Senthil T 2004 Phys. Rev. B 70 220403
[38]Wang C, Nahum A, Metlitski M A, Xu C and Senthil T 2017 Phys. Rev. X 7 031051
[39]Ma H and He Y C 2019 Phys. Rev. B 99 195130
[40]Ma R and Wang C 2019 arXiv:1912.12315
[41]Nahum A 2019 arXiv:1912.13468
[42]Gorbenko V, Rychkov S and Zan B 2018 J. High Energy Phys. 2018(10) 108
[43]Gorbenko V, Rychkov S and Zan B 2018 SciPost Phys. 5 050
[44]Patil P, Tang Y, Katz E and Sandvik A W 2017 Phys. Rev. B 96 045140
[45]Sandvik A W and Kurkijärvi J 1991 Phys. Rev. B 43 5950
[46]Sandvik A W 1992 J. Phys. A: Math. Gen. 25 3667
[47]Wang L, Beach K S D and Sandvik A W 2006 Phys. Rev. B 73 014431
[48]Sen A, Suwa H and Sandvik A W 2015 Phys. Rev. B 92 195145
[49]Campostrini M, Hasenbusch M, Pelissetto A, Rossi P and Vicari E 2002 Phys. Rev. B 65 144520
[50]Jiang F J and Wiese U J 2011 Phys. Rev. B 83 155120
[51]Iino S, Morita S, Kawashima N and Sandvik A W 2019 J. Phys. Soc. Jpn. 88 034006
[52]Nakayama Y and Ohtsuki T 2016 Phys. Rev. Lett. 117 131601
[53]Liu Y H, Wang Z J, Sato T, Hohenadler M, Wang C, Guo W A and Assaad F F 2019 Nat. Commun. 10 2658
Related articles from Frontiers Journals
[1] Zhi-Xuan Li, Shuai Yin, and Yu-Rong Shu. Imaginary-Time Quantum Relaxation Critical Dynamics with Semi-Ordered Initial States[J]. Chin. Phys. Lett., 2023, 40(3): 057502
[2] Kai-Yue Zeng, Fang-Yuan Song, Lang-Sheng Ling, Wei Tong, Shi-Liang Li, Zhao-Ming Tian, Long Ma, and Li Pi. Incommensurate Magnetic Order in Sm$_3$BWO$_9$ with Distorted Kagome Lattice[J]. Chin. Phys. Lett., 2022, 39(10): 057502
[3] Yanxing Yang, Kaiwen Chen, Zhaofeng Ding, Adrian D. Hillier, and Lei Shu. Muon Spin Relaxation Study of Frustrated Tm$_3$Sb$_3$Mg$_2$O$_{14}$ with Kagomé Lattice[J]. Chin. Phys. Lett., 2022, 39(10): 057502
[4] Ling Wang, Yalei Zhang, and Anders W. Sandvik. Quantum Spin Liquid Phase in the Shastry–Sutherland Model Detected by an Improved Level Spectroscopic Method[J]. Chin. Phys. Lett., 2022, 39(7): 057502
[5] Xinran Ma, Z. C. Tu, and Shi-Ju Ran. Deep Learning Quantum States for Hamiltonian Estimation[J]. Chin. Phys. Lett., 2021, 38(11): 057502
[6] Yuan Wei, Xiaoyan Ma, Zili Feng, Yongchao Zhang, Lu Zhang, Huaixin Yang, Yang Qi, Zi Yang Meng, Yan-Cheng Wang, Youguo Shi, and Shiliang Li. Nonlocal Effects of Low-Energy Excitations in Quantum-Spin-Liquid Candidate Cu$_3$Zn(OH)$_6$FBr[J]. Chin. Phys. Lett., 2021, 38(9): 057502
[7] Sizhuo Yu, Yuan Gao, Bin-Bin Chen, and Wei Li. Learning the Effective Spin Hamiltonian of a Quantum Magnet[J]. Chin. Phys. Lett., 2021, 38(9): 057502
[8] Ren-Gui Zhu. Classical Ground State Spin Ordering of the Antiferromagnetic $J_1$–$J_2$ Model[J]. Chin. Phys. Lett., 2019, 36(6): 057502
[9] Erhan Albayrak. The Mixed Spin-1/2 and Spin-1 Ising–Heisenberg Model in the Mean-Field Approximation: a New Approach[J]. Chin. Phys. Lett., 2018, 35(3): 057502
[10] Zhong-Chao Wei, Hai-Jun Liao, Jing Chen, Hai-Dong Xie, Zhi-Yuan Liu, Zhi-Yuan Xie, Wei Li, B. Normand, Tao Xiang. Self-Consistent Spin-Wave Analysis of the 1/3 Magnetization Plateau in the Kagome Antiferromagnet[J]. Chin. Phys. Lett., 2016, 33(07): 057502
[11] Da-Chuang Li, Xian-Ping Wang, Hu Li, Xiao-Man Li, Ming Yang, Zhuo-Liang Cao. Effects of Pure Dzyaloshinskii–Moriya Interaction with Magnetic Field on Entanglement in Intrinsic Decoherence[J]. Chin. Phys. Lett., 2016, 33(05): 057502
[12] DAI Jia, WANG Peng-Shuai, SUN Shan-Shan, PANG Fei, ZHANG Jin-Shan, DONG Xiao-Li, YUE Gen, JIN Kui, CONG Jun-Zhuang, Sun Yang, YU Wei-Qiang. Nuclear-Magnetic-Resonance Properties of the Staircase Kagomé Antiferromagnet $PbCu_3TeO_7$[J]. Chin. Phys. Lett., 2015, 32(12): 057502
[13] Faizi E., Eftekhari H.. Quantum Correlations in Ising-XYZ Diamond Chain Structure under an External Magnetic Field[J]. Chin. Phys. Lett., 2015, 32(10): 057502
[14] LI Da-Chuang, LI Xiao-Man, LI Hu, TAO Rui, YANG Ming, CAO Zhuo-Liang. Thermal Entanglement in the Pure Dzyaloshinskii–Moriya Model with Magnetic Field[J]. Chin. Phys. Lett., 2015, 32(5): 057502
[15] YANG Ge, CHEN Bin. Villain Transformation for Ferrimagnetic Spin Chain[J]. Chin. Phys. Lett., 2014, 31(06): 057502
Viewed
Full text


Abstract