Please wait a minute...
Chin. Phys. B, 2022, Vol. 31(7): 070502    DOI: 10.1088/1674-1056/ac4bd1
GENERAL Prev   Next  

Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model

Yan-Wei Dai(代艳伟)1,†, Sheng-Hao Li(李生好)1,2, and Xi-Hao Chen(陈西浩)1,3
1 Centre for Modern Physics and Department of Physics, Chongqing University, Chongqing 400044, China;
2 Chongqing Vocational Institute of Engineering, Chongqing 402260, China;
3 Research Institute for New Materials and Technology, Chongqing University of Arts and Sciences, Chongqing 400000, China
Abstract  We investigate quantum phase transitions for q-state quantum Potts models (q=2,3,4) on a square lattice and for the Ising model on a honeycomb lattice by using the infinite projected entangled-pair state algorithm with a simplified updating scheme. We extend the universal order parameter to a two-dimensional lattice system, which allows us to explore quantum phase transitions with symmetry-broken order for any translation-invariant quantum lattice system of the symmetry group G. The universal order parameter is zero in the symmetric phase, and it ranges from zero to unity in the symmetry-broken phase. The ground-state fidelity per lattice site is computed, and a pinch point is identified on the fidelity surface near the critical point. The results offer another example highlighting the connection between (i) critical points for a quantum many-body system undergoing a quantum phase-transition and (ii) pinch points on a fidelity surface. In addition, we discuss three quantum coherence measures: the quantum Jensen-Shannon divergence, the relative entropy of coherence, and the l1 norm of coherence, which are singular at the critical point, thereby identifying quantum phase transitions.
Keywords:  quantum phase transitions      universal order parameter      fidelity  
Received:  07 October 2021      Revised:  02 December 2021      Accepted manuscript online:  17 January 2022
PACS:  05.30.Rt (Quantum phase transitions)  
  75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.))  
  03.67.-a (Quantum information)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11805285), Natural Science Foundation of Chongqing of China (Grant No. cstc2020jcyjmsxmX0034), and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN 201900703).
Corresponding Authors:  Yan-Wei Dai     E-mail:

Cite this article: 

Yan-Wei Dai(代艳伟), Sheng-Hao Li(李生好), and Xi-Hao Chen(陈西浩) Universal order-parameter and quantum phase transition for two-dimensional q-state quantum Potts model 2022 Chin. Phys. B 31 070502

[1] Sachdev S 1999 Quantum Phase Transitions (Cambridge:Cambridge University Press)
[2] Vidal G 2007 Phys. Rev. Lett. 98 070201
[3] Orús R and Vidal G 2008 Phys. Rev. B 78 155117
[4] Jordan J, Orús R, Vidal G, Verstraete F and Cirac J I 2008 Phys. Rev. Lett. 101 250602
[5] Vidal G 2007 Phys. Rev. Lett. 99 220405
[6] Evenbly G and Vidal G 2009 Phys. Rev. B 79 144108
[7] Jiang H C, Wang Z Y and Xiang T 2008 Phys. Rev. Lett. 101 090603
[8] Huang R Z, Liao H J, Liu Z Y, Xie H D, Xie Z Y, Zhao H H, Chen J and Xiang T 2018 Chin. Phys. B 27 070501
[9] Xie Z Y, Chen J, Yu J F, Kong X, Normand B and Xiang T 2014 Phys. Rev. X 4 011025
[10] Liu W Y, Huang Y Z, Gong S S and Gu Z C 2021 Phys. Rev. B 103 235155
[11] Scarpa G, Molnár A, Ge Y, García-Ripoll J J, Schuch N, Pérez-García D and Iblisdir S 2020 Phys. Rev. Lett. 125 210504
[12] Schmoll P and Orús R 2020 Phys. Rev. B 102 241101
[13] Wen X G 2004 Quantum Field Theory of Many-Body Systems (Oxford:Oxford University Press)
[14] Wen X G and Wu Y S 1993 Phys. Rev. Lett. 70 1501
[15] Senthil T, Vishwanath A, Balents L, Sachdev S and Fisher M P A 2004 Science 303 1490
[16] Ran Y and Wen X G 2006 Phys. Rev. Lett. 96 026802
[17] Liu J H, Shi Q Q, Wang H L and Zhou H Q 2012 Phys. Rev. E 86 020102
[18] Shi Q Q, Zhou H Q and Batchelor M T 2015 Sci. Rep. 5 7673
[19] Zhou H Q and Barjaktarevic J P 2008 J. Phys. A:Math. Theor. 41 412001
[20] Zhou H Q 2007 arXiv:0704.2945
[21] Zhou H Q, Zhao J H and Li B 2008 J. Phys. A 41 492002
[22] Zhao J H, Wang H L, Li B and Zhou H Q 2010 Phys. Rev. E 82 061127
[23] Dai Y W, Hu B Q and Zhao J H 2010 J. Phys. A 43 372001
[24] Wang H L, Dai Y W, Hu B Q and Zhou H Q 2011 Phys. Lett. A 375 4045
[25] Su Y H, Hu B Q, Li S H and Cho S Y 2013 Phys. Rev. E 88 032110
[26] Zhou H Q, Orús R and Vidal G 2008 Phys. Rev. Lett. 100 080601
[27] Dai Y W, Cho S Y, Batchelor M T and Zhou H Q 2014 Phys. Rev. E 89 062142
[28] Li S H, Wang H L, Shi Q Q and Zhou H Q 2011 arXiv:1105.3008
[29] Baumgratz T, Cramer M and Plenio M B 2014 Phys. Rev. Lett. 113 140401
[30] Ma J, Yadin B, Girolami D, Vedral V and Gu M 2016 Phys. Rev. Lett. 116 160407
[31] Streltsov A, Singh U, Dhar H S, Bera M N and Adesso G 2015 Phys. Rev. Lett. 115 020403
[32] Tan K C, Kwon H, Park C Y and Jeong H 2016 Phys. Rev. A 94 022329
[33] Radhakrishnan C, Ermakov I and Byrnes T 2017 Phys. Rev. A 96 012341
[34] Orus R and Vidal G 2009 Phys. Rev. B 80 094403
[35] Solyom J and Pfeuty P 1981 Phys. Rev. B 24 218
[36] Wu F Y 1982 Rev. Mod. Phys. 54 235
[37] Hamer C J 2000 J. Phys. A 33 6683
[38] Hamer C J, Aydin M, Oitmaa J and He H X 1990 J. Phys. A 23 4025
[39] Blöte H W J and Deng Y 2002 Phys. Rev. E 66 066110
[40] Nienhuis B, Riedel E K and Schick M 1981 Phys. Rev. B 23 6055
[41] Gendiar A and Nishino T 2002 Phys. Rev. E 65 046702
[42] Nishino T, Hieida Y, Okunishi K, Maeshima N, Akutsu Y and Gendiar A 2001 Prog. Theor. Phys. 105 409
[43] Huang C J, Liu L, Jiang Y and Deng Y 2020 Phys. Rev. B 102 094101
[44] Hamer C J, Aydin M, Oitmaa J and He H X 1990 J. Phys. A 23 4025
[45] Blöte H W J and Deng Y 2002 Phys. Rev. E 66 066110
[1] Engineering topological state transfer in four-period Su—Schrieffer—Heeger chain
Xi-Xi Bao(包茜茜), Gang-Feng Guo(郭刚峰), and Lei Tan(谭磊). Chin. Phys. B, 2023, 32(2): 020301.
[2] Experimental realization of quantum controlled teleportation of arbitrary two-qubit state via a five-qubit entangled state
Xiao-Fang Liu(刘晓芳), Dong-Fen Li(李冬芬), Yun-Dan Zheng(郑云丹), Xiao-Long Yang(杨小龙), Jie Zhou(周杰), Yu-Qiao Tan(谭玉乔), and Ming-Zhe Liu(刘明哲). Chin. Phys. B, 2022, 31(5): 050301.
[3] Alternative non-Gaussianity measures for quantum states based on quantum fidelity
Cheng Xiang(向成), Shan-Shan Li(李珊珊), Sha-Sha Wen(文莎莎), and Shao-Hua Xiang(向少华). Chin. Phys. B, 2022, 31(3): 030306.
[4] Passively stabilized single-photon interferometer
Hai-Long Liu(刘海龙), Min-Jie Wang(王敏杰), Jia-Xin Bao(暴佳鑫), Chao Liu(刘超), Ya Li(李雅), Shu-Jing Li(李淑静), and Hai Wang(王海). Chin. Phys. B, 2022, 31(11): 110306.
[5] Controlled quantum teleportation of an unknown single-qutrit state in noisy channels with memory
Shexiang Jiang(蒋社想), Bao Zhao(赵宝), and Xingzhu Liang(梁兴柱). Chin. Phys. B, 2021, 30(6): 060303.
[6] Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
Guangyu Sun(孙光宇), Nvsen Ma(马女森), Bowen Zhao(赵博文), Anders W. Sandvik, and Zi Yang Meng(孟子杨). Chin. Phys. B, 2021, 30(6): 067505.
[7] Realization of adiabatic and diabatic CZ gates in superconducting qubits coupled with a tunable coupler
Huikai Xu(徐晖凯), Weiyang Liu(刘伟洋), Zhiyuan Li(李志远), Jiaxiu Han(韩佳秀), Jingning Zhang(张静宁), Kehuan Linghu(令狐克寰), Yongchao Li(李永超), Mo Chen(陈墨), Zhen Yang(杨真), Junhua Wang(王骏华), Teng Ma(马腾), Guangming Xue(薛光明), Yirong Jin(金贻荣), and Haifeng Yu(于海峰). Chin. Phys. B, 2021, 30(4): 044212.
[8] 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.
[9] Average fidelity estimation of twirled noisy quantum channel using unitary 2t-design
Linxi Zhang(张林曦), Changhua Zhu(朱畅华), Changxing Pei(裴昌幸). Chin. Phys. B, 2019, 28(1): 010304.
[10] Heavy fermions in high magnetic fields
M Smidman, B Shen(沈斌), C Y Guo(郭春煜), L Jiao(焦琳), X Lu(路欣), H Q Yuan(袁辉球). Chin. Phys. B, 2019, 28(1): 017106.
[11] Estimation of photon counting statistics with imperfect detectors
Xiao-Chuan Han(韩晓川), Dong-Wei Zhuang(庄东炜), Yu-Xuan Li(李雨轩), Jun-Feng Song(宋俊峰), Yong-Sheng Zhang(张永生). Chin. Phys. B, 2018, 27(7): 074208.
[12] Monogamy quantum correlation near the quantum phase transitions in the two-dimensional XY spin systems
Meng Qin(秦猛), Zhongzhou Ren(任中洲), Xin Zhang(张欣). Chin. Phys. B, 2018, 27(6): 060301.
[13] Identifying the closeness of eigenstates in quantum many-body systems
Hai-bin Li(李海彬), Yang Yang(杨扬), Pei Wang(王沛), Xiao-guang Wang(王晓光). Chin. Phys. B, 2017, 26(8): 080502.
[14] An intermediate state of T7 RNA polymerase provides another pathway of nucleotide selection
Zhan-Feng Wang(王展峰), Yu-Ru Liu(刘玉如), Peng-Ye Wang(王鹏业), Ping Xie(谢平). Chin. Phys. B, 2017, 26(10): 100203.
[15] Fidelity between Gaussian mixed states with quantum state quadrature variances
Hai-Long Zhang(张海龙), Chun Zhou(周淳), Jian-Hong Shi(史建红), Wan-Su Bao(鲍皖苏). Chin. Phys. B, 2016, 25(4): 040304.
No Suggested Reading articles found!