Abstract
In recent years, interacting topological insulators have emerged as new frontiers in condensed matter physics, and the hotly studied topological Kondo insulator (TKI) is one of such prototypes. Although its zero-temperature ground-state has been widely investigated, the finite temperature physics on TKI is largely unknown. Here, we explore the finite temperature properties in a simplified model for TKI, namely the one-dimensional p-wave periodic Anderson model, with numerically exact determinant quantum Monte Carlo simulation. It is found that the topological Haldane phase established for groundstate is still stable against small thermal fluctuation and its characteristic edge magnetization develops at low temperature. Such facts emphasize the robustness of (symmetry-protected) topological order against temperature effect, which always exists at real physical world. Moreover, we use the saturated low-T spin structure factor and the 1/T - law of susceptibility to detect the free edge spin moment, interestingly the low-temperature upturn behavior of the latter one is similar to experimental finding in SmB6 at T < 50 K. It implies that similar physical mechanism may work both for idealized models and realistic correlated electron materials. We have also identified an emergent energy scale Tcr, which signals a crossover into interesting low-T regime and seems to be the expected Ruderman–Kittel–Kasuya–Yosida coupling. Finally, the collective Kondo screening effect has been examined and it is heavily reduced at boundary, which may give a fruitful playground for novel physics beyond the wellestablished Haldane phase and topological band insulators.
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References
M. Z. Hasan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)
X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)
M. Hohenadler and F. F. Assaad, Correlation effects in two-dimensional topological insulators, J. Phys. Condens. Matter 25(14), 143201 (2013)
A. Bansil, H. Lin, and T. Das, Topological band theory, Rev. Mod. Phys. 88(2), 021004 (2016)
E. Witten, Fermion path integrals and topological phases, Rev. Mod. Phys. 88(3), 035001 (2016)
C. K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88(3), 035005 (2016)
T. Senthil, Symmetry-protected topological phases of quantum matter, Annu. Rev. Condens. Matter Phys. 6(1), 299 (2015)
C. X. Liu, S. C. Zhang, and X. L. Qi, The quantum anomalous Hall effect: Theory and experiment, Annu. Rev. Condens. Matter Phys. 7(1), 301 (2016)
M. Dzero, J. Xia, V. Galitski, and P. Coleman, Topological Kondo insulators, Annu. Rev. Condens. Matter Phys. 7(1), 249 (2016)
M. Dzero, K. Sun, V. Galitski, and P. Coleman, Topological Kondo insulators, Phys. Rev. Lett. 104(10), 106408 (2010)
J. Jiang, S. Li, T. Zhang, Z. Sun, F. Chen, Z. R. Ye, M. Xu, Q. Q. Ge, S. Y. Tan, X. H. Niu, M. Xia, B. P. Xie, Y. F. Li, X. H. Chen, H. H. Wen, and D. L. Feng, Observation of possible topological in-gap surface states in the Kondo insulator SmB6 by photoemission, Nat. Commun. 4(1), 3010 (2013)
M. Neupane, N. Alidoust, S. Y. Xu, T. Kondo, Y. Ishida, D. J. Kim, C. Liu, I. Belopolski, Y. J. Jo, T. R. Chang, H. T. Jeng, T. Durakiewicz, L. Balicas, H. Lin, A. Bansil, S. Shin, Z. Fisk, and M. Z. Hasan, Surface electronic structure of the topological Kondo-insulator candidate correlated electron system SmB6, Nat. Commun. 4(1), 2991 (2013)
V. Alexandrov, P. Coleman, and O. Erten, Kondo Breakdown in Topological Kondo Insulators, Phys. Rev. Lett. 114(17), 177202 (2015)
B. S. Tan, Y. T. Hsu, B. Zeng, M. C. Hatnean, N. Harrison, Z. Zhu, M. Hartstein, M. Kiourlappou, A. Srivastava, M. D. Johannes, T. P. Murphy, J. H. Park, L. Balicas, G. G. Lonzarich, G. Balakrishnan, and S. E. Sebastian, Unconventional Fermi surface in an insulating state, Science 349(6245), 287 (2015)
G. Baskaran, Majorana Fermi sea in insulating SmB6: A proposal and a theory of quantum oscillations in Kondo insulators, arXiv: 1507.03477
O. Erten, P. Y. Chang, P. Coleman, and A. M. Tsvelik, Skyrme Insulators: Insulators at the Brink of Superconductivity, Phys. Rev. Lett. 119(5), 057603 (2017)
A. Thomson and S. Sachdev, Fractionalized Fermi liquid on the surface of a topological Kondo insulator, Phys. Rev. B 93(12), 125103 (2016)
O. Erten, P. Ghaemi, and P. Coleman, Kondo breakdown and quantum oscillations in SmB6, Phys. Rev. Lett. 116(4), 046403 (2016)
D. Chowdhury, I. Sodemann, and T. Senthil, Mixedvalence insulators with neutral Fermi surfaces, Nat. Commun. 9(1), 1766 (2018)
I. Sodemann, D. Chowdhury, and T. Senthil, Quantum oscillations in insulators with neutral Fermi surfaces, Phys. Rev. B 97(4), 045152 (2018)
Y. Zhong, Y. Liu, and H.-G. Luo, Topological phase in 1D topological Kondo insulator: Z2 topological insulator, Haldane-like phase and Kondo breakdown, Eur. Phys. J. B 90, 147 (2017)
F. T. Lisandrini, A. M. Lobos, A. O. Dobry, and C. J. Gazza, Topological Kondo insulators in one dimension: Continuous Haldane-type ground-state evolution from the strongly interacting to the noninteracting limit, Phys. Rev. B 96(7), 075124 (2017)
X. G. Wen, Zoo of quantum-topological phases of matter, Rev. Mod. Phys. 89(4), 041004 (2017)
Y. F. Yang, Two-fluid model for heavy electron physics, Rep. Prog. Phys. 79(7), 074501 (2016)
R. Blankenbecler, D. J. Scalapino, and R. L. Sugar, Monte Carlo calculations of coupled boson-fermion systems (I), Phys. Rev. D 24(8), 2278 (1981)
J. E. Hirsch, Two-dimensional Hubbard model: Numerical simulation study, Phys. Rev. B 31(7), 4403 (1985)
R. R. dos Santo, Introduction to quantum Monte Carlo simulations for fermionic systems, Braz. J. Phys. 33, 1 (2003)
M. Vekic, J. W. Cannon, D. J. Scalapino, R. T. Scalettar, and R. L. Sugar, Competition between Antiferromagnetic Order and Spin-Liquid Behavior in the Two-Dimensional Periodic Anderson Model at Half Filling, Phys. Rev. Lett. 74(12), 2367 (1995)
M. Jiang, N. J. Curro, and R. T. Scalettar, Universal Knight shift anomaly in the periodic Anderson model, Phys. Rev. B 90(24), 241109(R) (2014)
H. F. Lin, H. S. Tao, W. X. Guo, and W. M. Liu, Antiferromagnetism and Kondo screening on a honeycomb lattice, Chin. Phys. B 24(5), 057101 (2015)
W. Hu, R. T. Scalettar, E. W. Huang, and B. Moritz, Effects of an additional conduction band on the singletantiferromagnet competition in the periodic Anderson model, Phys. Rev. B 95(23), 235122 (2017)
J. Gubernatis, N. Kawashima, and P. Werner, Quantum Monte Carlo Methods: Algorithms for Lattice Models, Cambridge University Press, 2016
T. Paiva, G. Esirgen, R. T. Scalettar, C. Huscroft, and A. K. McMahan, Doping-dependent study of the periodic Anderson model in three dimensions, Phys. Rev. B 68(19), 195111 (2003)
H. L. Nourse, I. P. McCulloch, C. Janani, and B. J. Powell, Haldane insulator protected by reflection symmetry in the doped Hubbard model on the three-legged ladder, Phys. Rev. B 94(21), 214418 (2016)
A. M. Lobos, A. O. Dobry, and V. Galitski, Magnetic end states in a strongly interacting one-dimensional topological Kondo Insulator, Phys. Rev. X 5(2), 021017 (2015)
A. Mezio, A. M. Lobos, A. O. Dobry, and C. J. Gazza, Haldane phase in one-dimensional topological Kondo insulators, Phys. Rev. B 92(20), 205128 (2015)
I. Hagymási and O. Legeza, Characterization of a correlated topological Kondo insulator in one dimension, Phys. Rev. B 93(16), 165104 (2016)
J. C. Nickerson, R. M. White, K. N. Lee, R. Bachmann, R. Geballe, and G. W. Hull, Physical properties of SmB6, Phys. Rev. B 3(6), 2030 (1971)
P. Coleman, Introduction to Many Body Physics, Chapters 15 to 18, Cambridge University Press, 2015
K. Kummer, S. Patil, A. Chikina, M. Güttler, M. Höppner, et al., Temperature-independent Fermi surface in the Kondo lattice YbRh2Si2, Phys. Rev. X 5(1), 011028 (2015)
Q. Y. Chen, D. F. Xu, X. H. Niu, J. Jiang, R. Peng, et al., Direct observation of how the heavy-fermion state develops in CeCoIn5, Phys. Rev. B 96(4), 045107 (2017)
E. Abrahams, J. Schmalian, and P. Wölfle, Strongcoupling theory of heavy-fermion criticality, Phys. Rev. B 90(4), 045105 (2014)
V. R. Shaginyan, A. Z. Msezane, G. S. Japaridze, K. G. Popov, and V. A. Khodel, Strongly correlated Fermi systems as a new state of matter, Front. Phys. 11(5), 117103 (2016)
Q. Si, S. Rabello, K. Ingersent, and J. L. Smith, Locally critical quantum phase transitions in strongly correlated metals, Nature 413(6858), 804 (2001)
T. Senthil, M. Vojta, and S. Sachdev, Weak magnetism and non-Fermi liquids near heavy-fermion critical points, Phys. Rev. B 69(3), 035111 (2004)
I. Paul, C. Pépin, and M. R. Norman, Kondo Breakdown and Hybridization Fluctuations in the Kondo-Heisenberg Lattice, Phys. Rev. Lett. 98(2), 026402 (2007)
Y. Zhong, K. Liu, Y. Q. Wang, and H. G. Luo, Alternative Kondo breakdown mechanism: Orbital-selective orthogonal metal transition, Phys. Rev. B Condens. Matter Mater. Phys. 86(11), 115113 (2012)
M. Hartstein, W. H. Toews, Y. T. Hsu, B. Zeng, X. Chen, et al., Fermi surface in the absence of a Fermi liquid in the Kondo insulator SmB6, Nat. Phys. 14(2), 166 (2017)
Y. Zhong, Y. Liu, and H. G. Luo, Simulating heavy fermion physics in optical lattice: Periodic Anderson model with harmonic trapping potential, Front. Phys. 12(5), 127502 (2017)
R. C. Caro, R. Franco, and J. Silva-Valencia, Spin-liquid state in an inhomogeneous periodic Anderson model, Phys. Rev. A 97(2), 023630 (2018)
Acknowledgements
This research was supported in part by the National Natural Science Foundation of China under Grant Nos. 11325417, 11674139, and 11704166, the Fundamental Research Funds for the Central Universities, Science Challenge Project under Grant No. JCKY2016212A502, SPC-Lab Research Fund (NO. XKFZ201605) and the Foundation of LCP.
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Zhong, Y., Wang, Q., Liu, Y. et al. Finite temperature physics of 1D topological Kondo insulator: Stable Haldane phase, emergent energy scale and beyond. Front. Phys. 14, 23602 (2019). https://doi.org/10.1007/s11467-018-0868-x
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DOI: https://doi.org/10.1007/s11467-018-0868-x