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In the numerical calculation, the projected entangled pair state (PEPS) algorithm is the most important tensor network algorithm for two-dimensional strongly correlated electron quantum lattice system. In this paper, the optimization of PEPS for two-dimensional quantum system is discussed. An optimization connection between how to update the PEPS tensor and how to calculate the physical observable is investigated, for the tensor network algorithm based on the PEPS representation, which can greatly improve the utilization of computing resources. In this case, optimized PEPS algorithm, as a powerful tool, can be used to study quantum phase transitions and quantum critical phenomena in the thermodynamic limit of the two-dimensional strongly correlated electron quantum lattice system. Of course, optimization of PEPS algorithm program has many other applications, such as adding U(1) and SO(2) symmetry in PEPS algorithm, etc.
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Keywords:
- projected entangled pair state /
- tensor network /
- strongly correlated electrons /
- quantum phase transition
[1] Wilson K G 1975 Rev. Mod. Phys. 47 773
[2] Krishnamurthy H R, Wilkins J W, Wilson K G 1980 Phys. Rev. B 21 1044
[3] Wilson K G 1971 Phys. Rev. B 4 3174
[4] Wilson K G 1971 Phys. Rev. B 4 3184
[5] White S R 1992 Phys. Rev. Lett. 69 2863
[6] White S R 1992 Phys. Rev. B 48 10345
[7] Ostlund S, Rommer S 1995 Phys. Rev. Lett. 75 3537
[8] Verstraete F, Porras D, Cirac J I 2004 Phys. Rev. Lett. 93 227205
[9] Vidal G 2007 Phys. Rev. Lett. 98 070201
[10] Murg V, Verstraete F, Cirac J I 2007 Phys. Rev. A 75 033605
[11] Jordan J, Orús R, Vidal G, Verstraete F, Cirac J I 2008 Phys. Rev. Lett. 101 250602
[12] Vidal G 2007 Phys. Rev. Lett. 99 220405
[13] Evenbly G, Vidal G 2009 Phys. Rev. B 79 144108
[14] Zhao J H, Wang H T 2012 Acta Phys. Sin. 61 220502 (in Chinese) [赵建辉, 王海涛 2012 61 220502]
[15] Shi Q Q, Li S H, Zhao J H, Zhou H Q 2009 arXiv: 0907.5520
[16] Li S H, Shi Q Q, Zhou H Q 2010 arXiv:1001.3343
[17] Li S H, Shi Q Q, Su Y H, Liu J H, Dai Y W, Zhou H Q 2012 Phys. Rev. B 86 064401
[18] Li B, Li S H, Zhou H Q 2009 Phys. Rev. E 79 060101(R)
[19] Li S H, Wang H L, Shi Q Q, Zhou H Q arXiv:1105.3008
[20] Wang H L, Shi Q Q, Li S H, Zhou H Q arXiv:1106.2129
[21] Corboz P, White S R, Vidal G, Troyer M 2011 Phys. Rev. B 84 041108(R)
[22] Murg V, Verstraete F, Cirac J I 2009 Phys. Rev. E 79 195119
[23] Orús R, Doherty A C, Vidal G 2009 Phys. Rev. Lett. 102 077203
[24] Bauer B, Vidal G, Troyer M 2009 J. Stat. Mech. 2009 P09006
[25] Zhou H Q, Orús R, Vidal G 2008 Phys. Rev. Lett. 100 080601
[26] Suzuki M 1990 Phys. Lett. A 146 319
[27] Suzuki M 1991 J. Math. Phys. 32 400
[28] Potts R B 1952 Proc. Cambridge Philos. Soc. 48 106
[29] Wu F Y 1982 Rev. Mod. Phys. 54 235
[30] Zhao J H 2012 Acta Phys. Sin. 61 220501 (in Chinese) [赵建辉 2012 61 220501]
[31] Wang B, Huang H L, Sun Z Y, Kou S P 2012 Chin. Phys. Lett. 29 120301
[32] Blote H W J, Deng Y 2002 Phys. Rev. E 66 066110
[33] Crawford J D 1991 Rev. Mod. Phys. 63 991
[34] Araki J, Yano T, Ueda M, Noda M T 1975 Proc. R. Soc. Lond. A 345 413
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[1] Wilson K G 1975 Rev. Mod. Phys. 47 773
[2] Krishnamurthy H R, Wilkins J W, Wilson K G 1980 Phys. Rev. B 21 1044
[3] Wilson K G 1971 Phys. Rev. B 4 3174
[4] Wilson K G 1971 Phys. Rev. B 4 3184
[5] White S R 1992 Phys. Rev. Lett. 69 2863
[6] White S R 1992 Phys. Rev. B 48 10345
[7] Ostlund S, Rommer S 1995 Phys. Rev. Lett. 75 3537
[8] Verstraete F, Porras D, Cirac J I 2004 Phys. Rev. Lett. 93 227205
[9] Vidal G 2007 Phys. Rev. Lett. 98 070201
[10] Murg V, Verstraete F, Cirac J I 2007 Phys. Rev. A 75 033605
[11] Jordan J, Orús R, Vidal G, Verstraete F, Cirac J I 2008 Phys. Rev. Lett. 101 250602
[12] Vidal G 2007 Phys. Rev. Lett. 99 220405
[13] Evenbly G, Vidal G 2009 Phys. Rev. B 79 144108
[14] Zhao J H, Wang H T 2012 Acta Phys. Sin. 61 220502 (in Chinese) [赵建辉, 王海涛 2012 61 220502]
[15] Shi Q Q, Li S H, Zhao J H, Zhou H Q 2009 arXiv: 0907.5520
[16] Li S H, Shi Q Q, Zhou H Q 2010 arXiv:1001.3343
[17] Li S H, Shi Q Q, Su Y H, Liu J H, Dai Y W, Zhou H Q 2012 Phys. Rev. B 86 064401
[18] Li B, Li S H, Zhou H Q 2009 Phys. Rev. E 79 060101(R)
[19] Li S H, Wang H L, Shi Q Q, Zhou H Q arXiv:1105.3008
[20] Wang H L, Shi Q Q, Li S H, Zhou H Q arXiv:1106.2129
[21] Corboz P, White S R, Vidal G, Troyer M 2011 Phys. Rev. B 84 041108(R)
[22] Murg V, Verstraete F, Cirac J I 2009 Phys. Rev. E 79 195119
[23] Orús R, Doherty A C, Vidal G 2009 Phys. Rev. Lett. 102 077203
[24] Bauer B, Vidal G, Troyer M 2009 J. Stat. Mech. 2009 P09006
[25] Zhou H Q, Orús R, Vidal G 2008 Phys. Rev. Lett. 100 080601
[26] Suzuki M 1990 Phys. Lett. A 146 319
[27] Suzuki M 1991 J. Math. Phys. 32 400
[28] Potts R B 1952 Proc. Cambridge Philos. Soc. 48 106
[29] Wu F Y 1982 Rev. Mod. Phys. 54 235
[30] Zhao J H 2012 Acta Phys. Sin. 61 220501 (in Chinese) [赵建辉 2012 61 220501]
[31] Wang B, Huang H L, Sun Z Y, Kou S P 2012 Chin. Phys. Lett. 29 120301
[32] Blote H W J, Deng Y 2002 Phys. Rev. E 66 066110
[33] Crawford J D 1991 Rev. Mod. Phys. 63 991
[34] Araki J, Yano T, Ueda M, Noda M T 1975 Proc. R. Soc. Lond. A 345 413
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