Quantum phase transitions in two-dimensional strongly correlated fermion systems

doi:10.1007/s11467-015-0498-5

Frontiers of Physics

2015, Vol. 10

Issue (5): 106401 https://doi.org/10.1007/s11467-015-0498-5

本期目录

Quantum phase transitions in two-dimensional strongly correlated fermion systems

Bao An（保安）^1,^3,^*(

),Chen Yao-Hua（陈耀华）²,Lin Heng-Fu（林恒福）²,Liu Hai-Di（刘海迪）²,Zhang Xiao-Zhong（章晓中）¹

1. Laboratory of Advanced Materials, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
2. Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
3. Key Laboratory of Integrated Exploitation of Bayan-Obo Multi-Metal Resources, Inner Mongolia University of Science & Technology, Baotou 014010, China

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Abstract：

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.

Key words： quantum phase transition two-dimensional lattices fermions cellular dynamical mean-field theory continuous-time quantum Monte Carlo

收稿日期: 2015-07-13 出版日期: 2015-10-26

Corresponding Author(s): Bao An（保安）

引用本文:

. [J]. Frontiers of Physics, 2015, 10(5): 106401.
Bao An（保安）,Chen Yao-Hua（陈耀华）,Lin Heng-Fu（林恒福）,Liu Hai-Di（刘海迪）,Zhang Xiao-Zhong（章晓中）. Quantum phase transitions in two-dimensional strongly correlated fermion systems. Front. Phys. , 2015, 10(5): 106401.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-015-0498-5
https://academic.hep.com.cn/fop/CN/Y2015/V10/I5/106401

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) https://doi.org/10.1080/00018739500101526
2	P. Fendley and K. Schoutens, Exact results for strongly correlated fermions in 2+1 dimensions, Phys. Rev. Lett. 95(4), 046403 (2005) https://doi.org/10.1103/PhysRevLett.95.046403
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) https://doi.org/10.1103/PhysRevB.45.3137
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) https://doi.org/10.1103/PhysRevB.58.R7475
5	K. M. O’Hara, , Observation of a strongly interacting degenerate Fermi gas of atoms, Science 298, 2179 (2002) https://doi.org/10.1126/science.1079107
6	E. Haller, R. Hart, M. J. Mark, J. G. Danzl, L. Reichsöllner, M. Gustavsson, M. Dalmonte, G. Pupillo, and H. C. Nägerl, Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons, Nature 466(7306), 597 (2010) https://doi.org/10.1038/nature09259
7	M. Capone, , Strongly correlated superconductivity, Science 296, 2364 (2002) https://doi.org/10.1126/science.1071122
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)
9	A. Ramirez, Strongly geometrically frustrated magnets, Annu. Rev. Mater. Sci. 24(1), 453 (1994) https://doi.org/10.1146/annurev.ms.24.080194.002321
10	Y. Yang and C. Thompson, Thermodynamics of the strongly correlated Hubbard model, J. Phys. Math. Gen. 24(6), L279 (1991) https://doi.org/10.1088/0305-4470/24/6/006
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) https://doi.org/10.1007/s11467-013-0359-z
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) https://doi.org/10.1007/s11467-013-0350-8
13	A. Lüscher and A. M. Läuchli, 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) https://doi.org/10.1103/PhysRevB.79.195102
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) https://doi.org/10.1139/p99-041
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) https://doi.org/10.1103/PhysRevLett.109.026404
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) https://doi.org/10.1103/PhysRevB.88.195130
17	D. Zanchi and H. Schulz, Weakly correlated electrons on a square lattice: Renormalization-group theory, Phys. Rev. B 61(20), 13609 (2000) https://doi.org/10.1103/PhysRevB.61.13609
18	K. Takeda, N. Uryû, 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) https://doi.org/10.1143/JPSJ.55.727
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) https://doi.org/10.1103/PhysRevB.74.085117
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) https://doi.org/10.1103/PhysRevLett.100.076402
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) https://doi.org/10.1103/PhysRevLett.103.036401
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) https://doi.org/10.1088/1674-1056/22/11/110309
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) https://doi.org/10.1103/PhysRevB.77.104413
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) https://doi.org/10.1103/PhysRevLett.91.107001
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) https://doi.org/10.1103/PhysRevB.78.024428
26	Y. L. Loh, D. X. Yao, and E. W. Carlson, Dimers on the triangular Kagome lattice, Phys. Rev. B 78(22), 224410 (2008) https://doi.org/10.1103/PhysRevB.78.224410
27	J. Zheng and G. Sun, Exact results for Ising models on the triangular Kagomé lattice, Phys. Rev. B 71(5), 052408 (2005) https://doi.org/10.1103/PhysRevB.71.052408
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) https://doi.org/10.1103/PhysRevLett.108.246402
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) https://doi.org/10.1103/PhysRevB.77.134402
30	A. Rüegg, J. Wen, and G. A. Fiete, Topological insulators on the decorated honeycomb lattice, Phys. Rev. B 81(20), 205115 (2010) https://doi.org/10.1103/PhysRevB.81.205115
31	H. D. Liu, , Antiferromagnetic metal and Mott transition on Shastry-Sutherland lattice, Sci. Rep. 4, 4829 (2014) https://doi.org/10.1038/srep04829
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) https://doi.org/10.1038/srep06918
33	M. Kargarian, and G. A. Fiete, Topological phases and phase transitions on the square-octagon lattice, Phys. Rev. B 82(8), 085106 (2010) https://doi.org/10.1103/PhysRevB.82.085106
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) https://doi.org/10.1088/0953-8984/25/30/305602
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) https://doi.org/10.1063/1.357006
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 andTechnology A: Molecular Crystals and Liquid Crystals 233(1), 317 (1993) https://doi.org/10.1080/10587259308054973
37	L. Balents, Spin liquids in frustrated magnets, Nature 464(7286), 199 (2010) https://doi.org/10.1038/nature08917
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) https://doi.org/10.1021/ja056666g
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) https://doi.org/10.1103/PhysRevLett.99.137202
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) https://doi.org/10.1103/PhysRevLett.82.3168
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) https://doi.org/10.1002/anie.201202598
42	M. R. He, R. Yu, and J. Zhu, Subangstrom profile imaging of relaxed ZnO(101 ¯0) surfaces., Nano Lett. 12(2), 704 (2012) https://doi.org/10.1021/nl2036172
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) https://doi.org/10.1103/PhysRevA.90.053627
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) https://doi.org/10.1103/PhysRevB.67.075110
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) https://doi.org/10.1103/PhysRevB.75.155113
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) https://doi.org/10.1088/1742-6596/150/4/042094
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) https://doi.org/10.1103/PhysRevLett.87.186401
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) https://doi.org/10.1103/PhysRevB.73.205106
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) https://doi.org/10.1103/PhysRevB.62.R9283
50	A. Liebsch, Correlated Dirac fermions on the honeycomb lattice studied within cluster dynamical mean field theory, Phys. Rev. B 83(3), 035113 (2011) https://doi.org/10.1103/PhysRevB.83.035113
51	O. Parcollet, G. Biroli, and G. Kotliar, Cluster dynamical mean field analysis of the Mott transition, Phys. Rev. Lett. 92(22), 226402 (2004) https://doi.org/10.1103/PhysRevLett.92.226402
52	H. Park, K. Haule, and G. Kotliar, Cluster dynamical mean field theory of the Mott transition, Phys. Rev. Lett. 101(18), 186403 (2008) https://doi.org/10.1103/PhysRevLett.101.186403
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) https://doi.org/10.1038/srep05367
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) https://doi.org/10.1103/RevModPhys.83.349
55	P. Kornilovitch, Continuous-time quantum Monte Carlo algorithm for the lattice polaron, Phys. Rev. Lett. 81(24), 5382 (1998) https://doi.org/10.1103/PhysRevLett.81.5382
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) https://doi.org/10.1103/PhysRevB.72.035122
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) https://doi.org/10.1103/PhysRevLett.97.076405
58	J. Hubbard, The dielectric theory of electronic interactions in solids, Proc. Phys. Soc. A 68(11), 976 (1955) https://doi.org/10.1088/0370-1298/68/11/304
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) https://doi.org/10.1098/rspa.1957.0106
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) https://doi.org/10.1098/rspa.1958.0003
61	J. Hubbard, Calculation of partition functions, Phys. Rev. Lett. 3(2), 77 (1959) https://doi.org/10.1103/PhysRevLett.3.77
62	J. Hubbard, Electron correlations in narrow energy bands, Proc. Royal Soc. Math. Phys. Eng. Sci. 276(1365), 238 (1963) https://doi.org/10.1098/rspa.1963.0204
63	J. Hubbard, Electron correlations in narrow energy bands (III): An improved solution, Proc. Royal Soc. Math. Phys. Eng. Sci. 281(1386), 401 (1964) https://doi.org/10.1098/rspa.1964.0190
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) https://doi.org/10.1016/0370-1573(95)00074-7

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