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.
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: daiyanwei1027@126.com
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. B78 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. B79 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. B27 070501 [9] Xie Z Y, Chen J, Yu J F, Kong X, Normand B and Xiang T 2014 Phys. Rev. X4 011025 [10] Liu W Y, Huang Y Z, Gong S S and Gu Z C 2021 Phys. Rev. B103 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. B102 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 Science303 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. E86 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. A41 492002 [22] Zhao J H, Wang H L, Li B and Zhou H Q 2010 Phys. Rev. E82 061127 [23] Dai Y W, Hu B Q and Zhao J H 2010 J. Phys. A43 372001 [24] Wang H L, Dai Y W, Hu B Q and Zhou H Q 2011 Phys. Lett. A375 4045 [25] Su Y H, Hu B Q, Li S H and Cho S Y 2013 Phys. Rev. E88 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. E89 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. A94 022329 [33] Radhakrishnan C, Ermakov I and Byrnes T 2017 Phys. Rev. A96 012341 [34] Orus R and Vidal G 2009 Phys. Rev. B80 094403 [35] Solyom J and Pfeuty P 1981 Phys. Rev. B24 218 [36] Wu F Y 1982 Rev. Mod. Phys.54 235 [37] Hamer C J 2000 J. Phys. A33 6683 [38] Hamer C J, Aydin M, Oitmaa J and He H X 1990 J. Phys. A23 4025 [39] Blöte H W J and Deng Y 2002 Phys. Rev. E66 066110 [40] Nienhuis B, Riedel E K and Schick M 1981 Phys. Rev. B23 6055 [41] Gendiar A and Nishino T 2002 Phys. Rev. E65 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. B102 094101 [44] Hamer C J, Aydin M, Oitmaa J and He H X 1990 J. Phys. A23 4025 [45] Blöte H W J and Deng Y 2002 Phys. Rev. E66 066110
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
