Quantum phase transitions in two-dimensional strongly correlated fermion systems

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.

Keywords

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

References

[1] T. Pruschke, M. Jarrell, and J. Freericks, Anomalous normal-state properties of high-T_c superconductors: Intrinsic properties of strongly correlated electron systems, Adv. Phys. 44(2), 187 (1995)

[2] P. Fendley and K. Schoutens, Exact results for strongly correlated fermions in 2+1 dimensions, Phys. Rev. Lett. 95(4), 046403 (2005)

[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)

[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)

[5] K. M. O’Hara, , Observation of a strongly interacting degenerate Fermi gas of atoms, Science 298, 2179 (2002)

[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)

[7] M. Capone, , Strongly correlated superconductivity, Science 296, 2364 (2002)

[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)

[10] Y. Yang and C. Thompson, Thermodynamics of the strongly correlated Hubbard model, J. Phys. Math. Gen. 24(6), L279 (1991)

[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)

[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)

[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)

[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)

[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)

[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)

[17] D. Zanchi and H. Schulz, Weakly correlated electrons on a square lattice: Renormalization-group theory, Phys. Rev. B 61(20), 13609 (2000)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[26] Y. L. Loh, D. X. Yao, and E. W. Carlson, Dimers on the triangular Kagome lattice, Phys. Rev. B 78(22), 224410 (2008)

[27] J. Zheng and G. Sun, Exact results for Ising models on the triangular Kagomé lattice, Phys. Rev. B 71(5), 052408 (2005)

[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)

[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)

[30] A. Rüegg, J. Wen, and G. A. Fiete, Topological insulators on the decorated honeycomb lattice, Phys. Rev. B 81(20), 205115 (2010)

[31] H. D. Liu, , Antiferromagnetic metal and Mott transition on Shastry-Sutherland lattice, Sci. Rep. 4, 4829 (2014)

[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)

[33] M. Kargarian, and G. A. Fiete, Topological phases and phase transitions on the square-octagon lattice, Phys. Rev. B 82(8), 085106 (2010)

[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)

[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)

[37] L. Balents, Spin liquids in frustrated magnets, Nature 464(7286), 199 (2010)

[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)

[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)

[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)

[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)

[42] M. R. He, R. Yu, and J. Zhu, Subangstrom profile imaging of relaxed ZnO(101 ¯0) surfaces., Nano Lett. 12(2), 704 (2012)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[50] A. Liebsch, Correlated Dirac fermions on the honeycomb lattice studied within cluster dynamical mean field theory, Phys. Rev. B 83(3), 035113 (2011)

[51] O. Parcollet, G. Biroli, and G. Kotliar, Cluster dynamical mean field analysis of the Mott transition, Phys. Rev. Lett. 92(22), 226402 (2004)

[52] H. Park, K. Haule, and G. Kotliar, Cluster dynamical mean field theory of the Mott transition, Phys. Rev. Lett. 101(18), 186403 (2008)

[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)

[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)

[55] P. Kornilovitch, Continuous-time quantum Monte Carlo algorithm for the lattice polaron, Phys. Rev. Lett. 81(24), 5382 (1998)

[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)

[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)

[58] J. Hubbard, The dielectric theory of electronic interactions in solids, Proc. Phys. Soc. A 68(11), 976 (1955)

[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)

[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)

[61] J. Hubbard, Calculation of partition functions, Phys. Rev. Lett. 3(2), 77 (1959)

[62] J. Hubbard, Electron correlations in narrow energy bands, Proc. Royal Soc. Math. Phys. Eng. Sci. 276(1365), 238 (1963)

[63] J. Hubbard, Electron correlations in narrow energy bands (III): An improved solution, Proc. Royal Soc. Math. Phys. Eng. Sci. 281(1386), 401 (1964)

[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)

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