Hubbard模型中的相位弦效应与交互Chern-Simons理论

张龙; 翁征宇

doi:10.7498/aps.64.217101

摘要

费米子符号在费米液体理论中至关重要. 然而, 在Mott绝缘体中, 很强的电子Coulomb相互作用抑制了体系的电荷涨落并消除了电子交换带来的费米子符号问题. 本文首先回顾二分晶格上Hubbard模型的相位弦理论, 从弱关联的费米液体到强关联的反铁磁Mott绝缘体的转变可以由此得到统一理解. 在任意Coulomb作用强度U下, 我们首先导出Hubbard模型的严格的符号结构. 在小U极限下, 它回到通常的费米子符号; 在大U极限下, 它给出了t-J模型的相位弦符号. 在半满情形下, 我们构造了一种电子分数化的表象, 其中, 电荷子与自旋子通过演生的交互Chern-Simons规范场相互耦合. 由此导出的基态波函数拟设与低能有效理论可以定性刻画Hubbard模型的基态相图. 在弱关联区域, 费米液体的准粒子由电荷子与自旋子的束缚态构成, 其长程相位相干性取决于背景自旋的关联性质. 体系的Mott转变可以通过电荷子打开能隙或是通过自旋子玻色凝聚来实现.

关键词:

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:

作者及机构信息

张龙,
翁征宇

1.
清华大学高等研究院, 北京 100084

通信作者: 翁征宇, weng@tsinghua.edu.cn

基金项目: 国家重点基础研究发展计划 (批准号: 2010CB923003) 资助的课题.

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).

参考文献

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[2]	Hubbard J 1963 Proc. R. Soc. A Math. Phys. Eng. Sci. 276 238
[3]	Roth W 1958 Phys. Rev. 110 1333
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[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

施引文献

[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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