Phase string effect and mutual Chern-Simons theory of Hubbard model

Zhang Long; Weng Zheng-Yu

doi:10.7498/aps.64.217101

Abstract

The fermion sign plays a dominant role in Fermi liquid theory. However, in Mott insulators, the strong Coulomb interaction suppresses the charge fluctuations and eliminates the fermion signs due to electron permutation. In this article, we first review the phase string theory of the Hubbard model for a bipartite lattice, which unifies the Fermi liquid at weak coupling and the antiferromagnetic Mott insulator at strong coupling. We first derive the exact sign structure of the Hubbard model for an arbitrary Coulomb interaction U. In small U limit, the conventional fermion sign is restored, while at large U limit, it leads to the phase string sign structure of the t-J model. For half filling, we construct an electron fractionalization representation, in which chargons and spinons are coupled to each other via emergent mutual Chern-Simons gauge fields. The corresponding ground state ansatz and low energy effective theory capture the ground state phase diagram of the Hubbard model qualitatively. For weak coupling regime, the Fermi liquid quasiparticle is formed by the bound state of a chargon and a spinon, and the long range phase coherence is determined by the background spin correlation. The Mott transition can be realized either by forming the chargon gap or by condensing the background spinons.

Keywords:

Authors and contacts

1.
Institute for Advanced Study, Tsinghua University, Beijing 100084, China

Corresponding author: Weng Zheng-Yu, weng@tsinghua.edu.cn

Funds: Project supported by the State Key Development Program for Basic Research of China (Grant No. 2010CB923003).

References

[1]	Mott N F 1949 Proc. Phys. Soc. A 62 416
[2]	Hubbard J 1963 Proc. R. Soc. A Math. Phys. Eng. Sci. 276 238
[3]	Roth W 1958 Phys. Rev. 110 1333
[4]	Anderson P W 1987 Science 235 1196
[5]	Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17
[6]	Wu K, Weng Z Y, Zaanen J 2008 Phys. Rev. B 77 155102
[7]	Sheng D N, Chen Y C, Weng Z Y 1996 Phys. Rev. Lett. 77 5102
[8]	Weng Z Y, Sheng D N, Chen Y C, Ting C S 1997 Phys. Rev. B 55 3894
[9]	Weng Z Y 2011 New J. Phys. 13 103039
[10]	Arovas D P, Auerbach A 1988 Phys. Rev. B 38 316
[11]	Auerbach A, Arovas D P 1988 Phys. Rev. Lett. 61 617
[12]	Zhang L, Weng Z Y 2014 Phys. Rev. B 90 165120
[13]	Yoshioka D 1989 J. Phys. Soc. Japan 58 32
[14]	Sarker S, Jayaprakash C, Krishnamurthy H R, Ma M 1989 Phys. Rev. B 40 5028
[15]	Affleck I, Marston J B 1988 Phys. Rev. B 37 3774
[16]	Marston J B, Affleck I 1989 Phys. Rev. B 39 11538
[17]	Rantner W, Wen X G 2002 Phys. Rev. B 66 144501
[18]	Marshall W 1955 Proc. R. Soc. London A 232 48
[19]	Yoshioka D 1989 J. Phys. Soc. Japan 58 1516
[20]	Weng Z Y, Muthukumar V N, Sheng D N, Ting C S 2001 Phys. Rev. B 63 075102
[21]	Zhu Z, Jiang H C, Qi Y, Tian C, Weng Z Y 2013 Sci. Rep. 3 2586
[22]	Liang S, Doucot B, Anderson P W 1988 Phys. Rev. Lett. 61 365
[23]	Kou S P, Qi X L, Weng Z Y 2005 Phys. Rev. B 71 235102
[24]	Ye P, Tian C S, Qi X L, Weng Z Y 2011 Phys. Rev. Lett. 106 147002
[25]	Ye P, Tian C S, Qi X L, Weng Z Y 2012 Nucl. Phys. B 854 815
[26]	Laughlin R B 1983 Phys. Rev. Lett. 50 1395
[27]	Kou S P, Levin M, Wen X G 2008 Phys. Rev. B 78 155134
[28]	Xu C, Sachdev S 2009 Phys. Rev. B 79 064405
[29]	Grover T, Senthil T 2008 Phys. Rev. Lett. 100 156804
[30]	Xu C, Sachdev S 2010 Phys. Rev. Lett. 105 057201
[31]	Zhang L, Weng Z Y 2015 unpublished
[32]	Oshikawa M 2000 Phys. Rev. Lett. 84 3370
[33]	Senthil T, Vishwanath A, Balents L, Sachdev S, Fisher M P A 2004 Science 303 1490
[34]	Senthil T, Balents L, Sachdev S, Vishwanath A, Fisher M P A 2004 Phys. Rev. B 70 144407
[35]	Herbut I F 2006 Phys. Rev. Lett. 97 146401
[36]	Herbut I F, Juričić V, Roy B 2009 Phys. Rev. B 79 085116
[37]	Assaad F F, Herbut I F 2013 Phys. Rev. X 3 031010
[38]	Anderson P W 1997 The theory of superconductivity in the high-Tc cuprate superconductors (NJ: Princeton University Press)
[39]	Moukouri S, Jarrell M 2001 Phys. Rev. Lett. 87 167010
[40]	Schäfer T, Geles F, Rost D, Rohringer G, Arrigoni E, Held K, Blmer N, Aichhorn M, Toschi A 2014 Phys. Rev. B 91 125109
[41]	Itou T, Oyamada A, Maegawa S, Tamura M, Kato R 2008 Phys. Rev. B 77 104413
[42]	Yamashita M, Nakata N, Senshu Y, Nagata M, Yamamoto H M, Kato R, Shibauchi T, Matsuda Y 2010 Science 328 1246
[43]	Yamashita S, Yamamoto T, Nakazawa Y, Tamura M, Kato R 2011 Nat. Commun. 2 275
[44]	Watanabe D, Yamashita M, Tonegawa S, Oshima Y, Yamamoto H M, Kato R, Sheikin I, Behnia K, Terashima T, Uji S, Shibauchi T, Matsuda Y 2012 Nat. Commun. 3 1090
[45]	Kanoda K, Kato R 2011 Annu. Rev. Condens. Matter Phys. 2 167
[46]	Shimizu Y, Miyagawa K, Kanoda K, Maesato M, Saito G 2006 Phys. Rev. B 73 140407
[47]	Yamashita S, Nakazawa Y, Oguni M, Oshima Y, Nojiri H, Shimizu Y, Miyagawa K, Kanoda K 2008 Nat. Phys. 4 459
[48]	Yamashita M, Nakata N, Kasahara Y, Sasaki T, Yoneyama N, Kobayashi N, Fujimoto S, Shibauchi T, Matsuda Y 2009 Nat. Phys. 5 44
[49]	Manna R S, de Souza M, Brhl A, Schlueter J A, Lang M 2010 Phys. Rev. Lett. 104 016403

Cited By

[1]	Mott N F 1949 Proc. Phys. Soc. A 62 416
[2]	Hubbard J 1963 Proc. R. Soc. A Math. Phys. Eng. Sci. 276 238
[3]	Roth W 1958 Phys. Rev. 110 1333
[4]	Anderson P W 1987 Science 235 1196
[5]	Lee P A, Nagaosa N, Wen X G 2006 Rev. Mod. Phys. 78 17
[6]	Wu K, Weng Z Y, Zaanen J 2008 Phys. Rev. B 77 155102
[7]	Sheng D N, Chen Y C, Weng Z Y 1996 Phys. Rev. Lett. 77 5102
[8]	Weng Z Y, Sheng D N, Chen Y C, Ting C S 1997 Phys. Rev. B 55 3894
[9]	Weng Z Y 2011 New J. Phys. 13 103039
[10]	Arovas D P, Auerbach A 1988 Phys. Rev. B 38 316
[11]	Auerbach A, Arovas D P 1988 Phys. Rev. Lett. 61 617
[12]	Zhang L, Weng Z Y 2014 Phys. Rev. B 90 165120
[13]	Yoshioka D 1989 J. Phys. Soc. Japan 58 32
[14]	Sarker S, Jayaprakash C, Krishnamurthy H R, Ma M 1989 Phys. Rev. B 40 5028
[15]	Affleck I, Marston J B 1988 Phys. Rev. B 37 3774
[16]	Marston J B, Affleck I 1989 Phys. Rev. B 39 11538
[17]	Rantner W, Wen X G 2002 Phys. Rev. B 66 144501
[18]	Marshall W 1955 Proc. R. Soc. London A 232 48
[19]	Yoshioka D 1989 J. Phys. Soc. Japan 58 1516
[20]	Weng Z Y, Muthukumar V N, Sheng D N, Ting C S 2001 Phys. Rev. B 63 075102
[21]	Zhu Z, Jiang H C, Qi Y, Tian C, Weng Z Y 2013 Sci. Rep. 3 2586
[22]	Liang S, Doucot B, Anderson P W 1988 Phys. Rev. Lett. 61 365
[23]	Kou S P, Qi X L, Weng Z Y 2005 Phys. Rev. B 71 235102
[24]	Ye P, Tian C S, Qi X L, Weng Z Y 2011 Phys. Rev. Lett. 106 147002
[25]	Ye P, Tian C S, Qi X L, Weng Z Y 2012 Nucl. Phys. B 854 815
[26]	Laughlin R B 1983 Phys. Rev. Lett. 50 1395
[27]	Kou S P, Levin M, Wen X G 2008 Phys. Rev. B 78 155134
[28]	Xu C, Sachdev S 2009 Phys. Rev. B 79 064405
[29]	Grover T, Senthil T 2008 Phys. Rev. Lett. 100 156804
[30]	Xu C, Sachdev S 2010 Phys. Rev. Lett. 105 057201
[31]	Zhang L, Weng Z Y 2015 unpublished
[32]	Oshikawa M 2000 Phys. Rev. Lett. 84 3370
[33]	Senthil T, Vishwanath A, Balents L, Sachdev S, Fisher M P A 2004 Science 303 1490
[34]	Senthil T, Balents L, Sachdev S, Vishwanath A, Fisher M P A 2004 Phys. Rev. B 70 144407
[35]	Herbut I F 2006 Phys. Rev. Lett. 97 146401
[36]	Herbut I F, Juričić V, Roy B 2009 Phys. Rev. B 79 085116
[37]	Assaad F F, Herbut I F 2013 Phys. Rev. X 3 031010
[38]	Anderson P W 1997 The theory of superconductivity in the high-Tc cuprate superconductors (NJ: Princeton University Press)
[39]	Moukouri S, Jarrell M 2001 Phys. Rev. Lett. 87 167010
[40]	Schäfer T, Geles F, Rost D, Rohringer G, Arrigoni E, Held K, Blmer N, Aichhorn M, Toschi A 2014 Phys. Rev. B 91 125109
[41]	Itou T, Oyamada A, Maegawa S, Tamura M, Kato R 2008 Phys. Rev. B 77 104413
[42]	Yamashita M, Nakata N, Senshu Y, Nagata M, Yamamoto H M, Kato R, Shibauchi T, Matsuda Y 2010 Science 328 1246
[43]	Yamashita S, Yamamoto T, Nakazawa Y, Tamura M, Kato R 2011 Nat. Commun. 2 275
[44]	Watanabe D, Yamashita M, Tonegawa S, Oshima Y, Yamamoto H M, Kato R, Sheikin I, Behnia K, Terashima T, Uji S, Shibauchi T, Matsuda Y 2012 Nat. Commun. 3 1090
[45]	Kanoda K, Kato R 2011 Annu. Rev. Condens. Matter Phys. 2 167
[46]	Shimizu Y, Miyagawa K, Kanoda K, Maesato M, Saito G 2006 Phys. Rev. B 73 140407
[47]	Yamashita S, Nakazawa Y, Oguni M, Oshima Y, Nojiri H, Shimizu Y, Miyagawa K, Kanoda K 2008 Nat. Phys. 4 459
[48]	Yamashita M, Nakata N, Kasahara Y, Sasaki T, Yoneyama N, Kobayashi N, Fujimoto S, Shibauchi T, Matsuda Y 2009 Nat. Phys. 5 44
[49]	Manna R S, de Souza M, Brhl A, Schlueter J A, Lang M 2010 Phys. Rev. Lett. 104 016403

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Vol. 64, Issue 21 - 2015-11-05

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