Quantum phase transitions in two-dimensional strongly correlated fermion systems
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  • 作者:An Bao 保安 ; Yao-Hua Chen 陈耀勿/a> ; Heng-Fu Lin 林恒礿/a> ; Hai-Di Liu 刘海轿/a>…
  • 关键词:quantum phase transition ; two ; dimensional lattices ; fermions ; cellular dynamical mean ; field theory ; continuous ; time quantum Monte Carlo
  • 刊名:Frontiers of Physics
  • 出版年:2015
  • 出版时间:October 2015
  • 年:2015
  • 卷:10
  • 期:5
  • 全文大小:1,702 KB
  • 参考文献:1.T. Pruschke, M. Jarrell, and J. Freericks, Anomalous normal-state properties of high-Tc superconductors: Intrinsic properties of strongly correlated electron systems, Adv. Phys. 44(2), 187 (1995)CrossRef ADS
    2.P. Fendley and K. Schoutens, Exact results for strongly correlated fermions in 2+1 dimensions, Phys. Rev. Lett. 95(4), 046403 (2005)CrossRef ADS
    3.W. Krauth, M. Caffarel, and J. P. Bouchaud, Gutzwiller wave function for a model of strongly interacting bosons, Phys. Rev. B 45(6), 3137 (1992)CrossRef ADS
    4.M. Hettler, A. N. Tahvildar-Zadeh, M. Jarrell, T. Pruschke, and H. R. Krishnamurthy, Nonlocal dynamical correlations of strongly interacting electron systems, Phys. Rev. B 58(12), R7475 (1998)CrossRef ADS
    5.K. M. O’Hara, et al., Observation of a strongly interacting degenerate Fermi gas of atoms, Science 298, 2179 (2002)CrossRef ADS
    6.E. Haller, R. Hart, M. J. Mark, J. G. Danzl, L. Reichsöllner, M. Gustavsson, M. Dalmonte, G. Pupillo, and H. C. Nagerl, Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons, Nature 466(7306), 597 (2010)CrossRef ADS
    7.M. Capone, et al., Strongly correlated superconductivity, Science 296, 2364 (2002)CrossRef ADS
    8.A. Georges, G. Kotliar, and Q. Si, Strongly correlated systems in infinite dimensions and their zero dimensional counterparts, Int. J. Mod. Phys. B 06(05n06), 705 (1992)MathSciNet CrossRef ADS
    9.A. Ramirez, Strongly geometrically frustrated magnets, Annu. Rev. Mater. Sci. 24(1), 453 (1994)CrossRef ADS
    10.Y. Yang and C. Thompson, Thermodynamics of the strongly correlated Hubbard model, J. Phys. Math. Gen. 24(6), L279 (1991)MathSciNet CrossRef ADS
    11.J. H. Wu, R. Qi, A. C. Ji, and W. M. Liu, Quantum tunneling of ultracold atoms in optical traps, Front. Phys. 9(2), 137 (2014)CrossRef
    12.S. W. Song, L. Wen, C. F. Liu, S. C. Gou, and W. M. Liu, Ground states, solitons and spin textures in spin-1 Bose–Einstein condensates, Front. Phys. 8(3), 302 (2013)CrossRef
    13.A. Lüscher and A. M. Lauchli, Exact diagonalization study of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field, Phys. Rev. B 79(19), 195102 (2009)CrossRef ADS
    14.D. Betts, H. Lin, and J. Flynn, Improved finite-lattice estimates of the properties of two quantum spin models on the infinite square lattice, Can. J. Phys. 77(5), 353 (1999)CrossRef ADS
    15.C. C. Chang and R. T. Scalettar, Quantum disordered phase near the Mott transition in the staggered-flux Hubbard model on a square lattice, Phys. Rev. Lett. 109(2), 026404 (2012)CrossRef ADS
    16.Y. H. Chen, J. Li, and C. S. Ting, Topological phase transitions with non-Abelian gauge potentials on square lattices, Phys. Rev. B 88(19), 195130 (2013)CrossRef ADS
    17.D. Zanchi and H. Schulz, Weakly correlated electrons on a square lattice: Renormalization-group theory, Phys. Rev. B 61(20), 13609 (2000)CrossRef ADS
    18.K. Takeda, N. Uryu, K. Ubukoshi, and K. Hirakawa, Critical exponents in the frustrated Heisenberg antiferromagnet with layered-triangular lattice: VBr2, J. Phys. Soc. Jpn. 55(3), 727 (1986)CrossRef ADS
    19.K. Aryanpour, W. E. Pickett, and R. T. Scalettar, Dynamical mean-field study of the Mott transition in the half-filled Hubbard model on a triangular lattice, Phys. Rev. B 74(8), 085117 (2006)CrossRef ADS
    20.T. Ohashi, T. Momoi, H. Tsunetsugu, and N. Kawakami, Finite temperature Mott transition in Hubbard model on anisotropic triangular lattice, Phys. Rev. Lett. 100(7), 076402 (2008)CrossRef ADS
    21.T. Yoshioka, A. Koga, and N. Kawakami, Quantum phase transitions in the Hubbard model on a triangular lattice, Phys. Rev. Lett. 103(3), 036401 (2009)CrossRef ADS
    22.A. Bao, Y. H. Chen, and X. Z. Zhang, Quantum phase transitions of fermionic atomsin an anisotropic triangular optical lattice., Chin. Phys. B 22(11), 110309 (2013)CrossRef ADS
    23.T. Itou, A. Oyamada, S. Maegawa, M. Tamura, and R. Kato, Quantum spin liquid in the spin-1/2 triangular antiferromagnet EtMe3Sb[Pd(dmit)2]2, Phys. Rev. B 77(10), 104413 (2008)CrossRef ADS
    24.Y. Shimizu, K. Miyagawa, K. Kanoda, M. Maesato, and G. Saito, Spin liquid state in an organic Mott insulator with a triangular lattice, Phys. Rev. Lett. 91(10), 107001 (2003)CrossRef ADS
    25.D. X. Yao, Y. L. Loh, E. W. Carlson, and M. Ma, XXZ and Ising spins on the triangular Kagome lattice, Phys. Rev. B 78(2), 024428 (2008)CrossRef ADS
    26.Y. L. Loh, D. X. Yao, and E. W. Carlson, Dimers on the triangular Kagome lattice, Phys. Rev. B 78(22), 224410 (2008)CrossRef ADS
    27.J. Zheng and G. Sun, Exact results for Ising models on the triangular Kagomé lattice, Phys. Rev. B 71(5), 052408 (2005)CrossRef ADS
    28.Y. H. Chen, H. S. Tao, D. X. Yao, and W. M. Liu, Kondo metal and ferrimagnetic insulator on the triangular Kagome lattice, Phys. Rev. Lett. 108(24), 246402 (2012)CrossRef ADS
    29.Y. L. Loh, D. X. Yao, and E. W. Carlson, Thermodynamics of Ising spins on the triangular Kagome lattice: Exact analytical method and Monte Carlo simulations, Phys. Rev. B 77(13), 134402 (2008)CrossRef ADS
    30.A. Rüegg, J. Wen, and G. A. Fiete, Topological insulators on the decorated honeycomb lattice, Phys. Rev. B 81(20), 205115 (2010)CrossRef ADS
    31.H. D. Liu, et al., Antiferromagnetic metal and Mott transition on Shastry-Sutherland lattice, Sci. Rep. 4, 4829 (2014)ADS
    32.A. Bao, H. S. Tao, H. D. Liu, X. Z. Zhang, and W. M. Liu, Quantum magnetic phase transition in square-octagon lattice, Sci. Rep. 4, 6918 (2014)CrossRef ADS
    33.M. Kargarian, and G. A. Fiete, Topological phases and phase transitions on the square-octagon lattice, Phys. Rev. B 82(8), 085106 (2010)CrossRef ADS
    34.X. P. Liu, W. C. Chen, Y. F. Wang, and C. D. Gong, Topological quantum phase transitions on the kagome and squareoctagon lattices, J. Phys.: Condens. Matter 25(30), 305602 (2013)
    35.S. Maruti and L. W. ter Haar, Magnetic properties of the two-dimensional “triangles-in-triangles” Kagomé lattice Cu9X2(cpa)6 (X=F,Cl,Br), J. Appl. Phys. 75(10), 5949 (1994)CrossRef ADS
    36.M. Gonzalez, F. Cervantes-lee, and L. W. ter Haar, Structural and magnetic properties of the topologically novel 2-D material Cu9F2 cpa)6: A triangulated Kagome - like hexagonal network of Cu(II) trimers interconnected by Cu(II) monomers, Molecular Crystals and Liquid Crystals Science and Technology A: Molecular Crystals and Liquid Crystals 233(1), 317 (1993)CrossRef
    37.L. Balents, Spin liquids in frustrated magnets, Nature 464(7286), 199 (2010)CrossRef ADS
    38.M. P. Shores, B. M. Bartlett, and D. G. Nocera, Spinfrustrated organic-inorganic hybrids of Lindgrenite, J. Am. Chem. Soc. 127(51), 17986 (2005)CrossRef
    39.M. Sasaki, K. Hukushima, H. Yoshino, and H. Takayama, Scaling analysis of domain-wall free energy in the Edwards–Anderson Ising spin glass in a magnetic field, Phys. Rev. Lett. 99(13), 137202 (2007)CrossRef ADS
    40.H. Kageyama, K. Yoshimura, R. Stern, N. V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C. P. Slichter, T. Goto, and Y. Ueda, Exact Dimer ground state and quantized magnetization plateaus in the two-dimensional spin system SrCu2(BO3)2, Phys. Rev. Lett. 82(15), 3168 (1999)CrossRef ADS
    41.M. R. He, R. Yu, and J. Zhu, Reversible wurtzite-tetragonal reconstruction in ZnO(1010) surfaces, Angew. Chem. Int. Ed. Engl. 51(31), 7744 (2012)CrossRef
    42.M. R. He, R. Yu, and J. Zhu, Subangstrom profile imaging of relaxed ZnO(1010) surfaces., Nano Lett. 12(2), 704 (2012)CrossRef ADS
    43.H. F. Lin, Y. H. Chen, H. D. Liu, H. S. Tao, and W. M. Liu, Mott transition and antiferromagnetism of cold fermions in the decorated honeycomb lattice, Phys. Rev. A 90(5), 053627 (2014)CrossRef ADS
    44.C. J. Bolech, S. S. Kancharla, and G. Kotliar, Cellular dynamical mean-field theory for the one-dimensional extended Hubbard model, Phys. Rev. B 67(7), 075110 (2003)CrossRef ADS
    45.K. Haule, Quantum Monte Carlo impurity solver for cluster dynamical mean-field theory and electronic structure calculations with adjustable cluster base, Phys. Rev. B 75(15), 155113 (2007)CrossRef ADS
    46.T. Kita, T. Ohashi, and S. Suga, Spatial fluctuations of spin and orbital in two-orbital Hubbard model: cluster dynamical mean field study, J. Phys. Conf. Ser. 150(4), 042094 (2009)CrossRef ADS
    47.G. Kotliar, S. Y. Savrasov, G. Pálsson, and G. Biroli, Cellular dynamical mean field approach to strongly correlated systems, Phys. Rev. Lett. 87(18), 186401 (2001)CrossRef ADS
    48.B. Kyung, G. Kotliar, and A. M. S. Tremblay, Quantum Monte Carlo study of strongly correlated electrons: Cellular dynamical mean-field theory, Phys. Rev. B 73(20), 205106 (2006)CrossRef ADS
    49.A. Lichtenstein and M. Katsnelson, Antiferromagnetism and d-wave superconductivity in cuprates: A cluster dynamical mean-field theory, Phys. Rev. B 62(14), R9283 (2000)CrossRef ADS
    50.A. Liebsch, Correlated Dirac fermions on the honeycomb lattice studied within cluster dynamical mean field theory, Phys. Rev. B 83(3), 035113 (2011)CrossRef ADS
    51.O. Parcollet, G. Biroli, and G. Kotliar, Cluster dynamical mean field analysis of the Mott transition, Phys. Rev. Lett. 92(22), 226402 (2004)CrossRef ADS
    52.H. Park, K. Haule, and G. Kotliar, Cluster dynamical mean field theory of the Mott transition, Phys. Rev. Lett. 101(18), 186403 (2008)CrossRef ADS
    53.H. S. Tao, Y. H. Chen, H. F. Lin, H. D. Liu, and W. M. Liu, Layer anti-ferromagnetism on bilayer honeycomb lattice, Sci. Rep. 4, 5367 (2014)ADS
    54.E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Continuous-time Monte Carlo methods for quantum impurity models, Rev. Mod. Phys. 83(2), 349 (2011)CrossRef ADS
    55.P. Kornilovitch, Continuous-time quantum Monte Carlo algorithm for the lattice polaron, Phys. Rev. Lett. 81(24), 5382 (1998)CrossRef ADS
    56.A. N. Rubtsov, V. V. Savkin, and A. I. Lichtenstein, Continuous-time quantum Monte Carlo method for fermions, Phys. Rev. B 72(3), 035122 (2005)CrossRef ADS
    57.P. Werner, A. Comanac, L. de’ Medici, M. Troyer, and A. J. Millis, Continuous-time solver for quantum impurity models, Phys. Rev. Lett. 97(7), 076405 (2006)CrossRef ADS
    58.J. Hubbard, The dielectric theory of electronic interactions in solids, Proc. Phys. Soc. A 68(11), 976 (1955)CrossRef ADS
    59.J. Hubbard, The description of collective motions in terms of many-body perturbation theory, Proc. Royal Soc. Math. Phys. Eng. Sci. 240(1223), 539 (1957)MathSciNet CrossRef MATH
    60.J. Hubbard, The description of collective motions in terms of many-body perturbation theory (II): The correlation energy of a free-electron gas, Proc. Royal Soc. Math. Phys. Eng. Sci. 243(1234), 336 (1958)MathSciNet CrossRef MATH
    61.J. Hubbard, Calculation of partition functions, Phys. Rev. Lett. 3(2), 77 (1959)MathSciNet CrossRef ADS
    62.J. Hubbard, Electron correlations in narrow energy bands, Proc. Royal Soc. Math. Phys. Eng. Sci. 276(1365), 238 (1963)CrossRef
    63.J. Hubbard, Electron correlations in narrow energy bands (III): An improved solution, Proc. Royal Soc. Math. Phys. Eng. Sci. 281(1386), 401 (1964)CrossRef
    64.M. Jarrell and J. E. Gubernatis, Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data, Phys. Rep. 269(3), 133 (1996)MathSciNet CrossRef ADS
  • 作者单位:An Bao 保安 (1) (3)
    Yao-Hua Chen 陈耀华 (2)
    Heng-Fu Lin 林恒福 (2)
    Hai-Di Liu 刘海迪 (2)
    Xiao-Zhong Zhang 章晓中 (1)

    1. Laboratory of Advanced Materials, School of Materials Science and Engineering, Tsinghua University, Beijing, 100084, China
    3. Key Laboratory of Integrated Exploitation of Bayan-Obo Multi-Metal Resources, Inner Mongolia University of Science & Technology, Baotou, 014010, China
    2. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China
  • 刊物类别:Physics and Astronomy
  • 刊物主题:Physics
    Chinese Library of Science
  • 出版者:Higher Education Press, co-published with Springer-Verlag GmbH
  • ISSN:2095-0470
文摘
In this article, we review our recent work on quantum phase transition in two-dimensional strongly correlated fermion systems. We discuss the metal–insulator transition properties of these systems by calculating the density of states, double occupancy, and Fermi surface evolution using a combination of the cellular dynamical mean-field theory (CDMFT) and the continuous-time quantum Monte Carlo algorithm. Furthermore, we explore the magnetic properties of each state by defining magnetic order parameters. Rich phase diagrams with many intriguing quantum states, including antiferromagnetic metal, paramagnetic metal, Kondo metal, and ferromagnetic insulator, were found for the two-dimensional lattices with strongly correlated fermions. We believe that our results would lead to a better understanding of the properties of real materials.
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