Title

量子自旋冰系統在二維竹篩晶格上之古典自旋液態

Translated Titles

Classical spin liquid state in quantum kagome ice

DOI

10.6342/NTU201801820

Authors

吳愷訢

Key Words

量子自旋液態 ; 挫折系統 ; 量子蒙地卡羅演算法 ; Quantum spin liquid ; frustrated system ; Quantum Monte-Carlo

PublicationName

臺灣大學物理學研究所學位論文

Volume or Term/Year and Month of Publication

2018年

Academic Degree Category

碩士

Advisor

高英哲

Content Language

英文

Chinese Abstract

在此篇論文裏,我們利用量子蒙地卡羅演算法對二維竹篩晶系上,半整數自旋海森堡XYZh模型做深入的數值模擬計算研究。 近期理論分析對於XYZh模型這樣的一個挫折系統之研究提出了具有實現Z2拓撲有序之量子自旋液態的可能性。 在數值模擬研究方面,近期對於XYZh模型在竹篩晶格上的計算發現了一個在極低溫仍具有磁無序性的特殊物質態。 這種極低溫仍保有磁無序的特性使其被認為極有可能就是理論上預測的Z2拓撲有序之量子自旋態。 然而目前研究仍沒有直接證據支持此推論。 此篇論文之研究即針對這樣的一個磁無序物質態做深入的數值探討。 我們對此態的拓撲熵以及熱力學熵之量子蒙卡計算結果指出此態不具有拓撲有序,即不為先前理論預測的Z2拓撲有序之量子自旋液態。 而熱力學熵計算結果指向此態在極低溫依然為具有古典行為的自旋冰態。 在對XYZh模型更深入的理論分析,我們發現其存在非典型的微擾拮抗機制使得量子微擾效應對系統的古典行為做了強化。 此現象在我們的量子模擬計算結果中得到了驗證。 這種強化古典行為的非典型量子效應是一個非常稀少的例子。 此機制的發現為量子磁性系統提出了一個新的研究方向。

English Abstract

We study the spin-1/2 Heisenberg XYZh model on a kagome lattice with quantum Monte Carlo (QMC) simulation. Recently, the model is proposed to host the Z2 quantum spin liquid (QSL) with a Z2 topological order. Numerical studies found a quantum kagome ice state which lacks long-range order. This suggests the possibility for the state to be a Z2 QSL. However, no direct evidence of Z2 QSL is shown. Here, we carefully examine the XYZh model. By measuring the topological entanglement entropy using quantum Monte Carlo simulation, we find that, contrary to previous beliefs, the state has no Z2 topological order. Instead, the system behaves like a classical kagome ice down to a very low temperature. Our theoretical analysis indicates that an intricate competition of the off-diagonal and non-trivial diagonal perturbation contributions suppresses the quantum energy scale. This leads to a quasi-degenerate picture where the system remains classical. The scenario is supported with the measurement of hexagon fractions using QMC. This is a rare example of a quantum model that remains classical down to a very low temperature that is due to quantum tunneling effect. The mechanism opens a way to engineer quantum-to-classical crossover in quantum magnets.

Topic Category 基礎與應用科學 > 物理
理學院 > 物理學研究所
Reference
  1. [1] J. H. Barry, M. Khatun, and T. Tanaka. Exact solutions for Ising-model even-number correlations on planar lattices. Phys. Rev. B, 37:5193–5204, Apr 1988.
  2. [2] O. Benton. Quantum origins of moment fragmentation in Nd2Zr2O7. Phys. Rev. B, 94:104430, Sep 2016.
  3. [3] O. Benton, O. Sikora, and N. Shannon. Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice. Phys. Rev. B, 86:075154, Aug 2012.
  4. [4] D. L. Bergman, R. Shindou, G. A. Fiete, and L. Balents. Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet. Phys. Rev. B, 75:094403, Mar 2007.
  5. [5] D. L. Bergman, R. Shindou, G. A. Fiete, and L. Balents. Effective Hamiltonians for some highly frustrated magnets. Journal of Physics: Condensed Matter, 19(14):145204, 2007.
  6. [6] J. G. Brankov, D. M. Danchev, and N. S. Tonchev. Theory of critical phenomena in finite-size systems: scaling and quantum effects, volume 9. World Scientific, 2000.
  7. [7] S. Burkhardt. Efficiency of parallel tempering for Ising systems. M.S. Thesis, 2010.
  8. [8] J. Carrasquilla, Z. Hao, and R. G. Melko. A two-dimensional spin liquid in quantum kagome ice. Nature communications, 6:7421, 2015.
  9. [9] J. I. Cirac, D. Poilblanc, N. Schuch, and F. Verstraete. Entanglement spectrum and boundary theories with projected entangled-pair states. Phys. Rev. B, 83:245134, Jun 2011.
  10. [10] K. Damle and T. Senthil. Spin nematics and magnetization plateau transition in anisotropic kagome magnets. Phys. Rev. Lett., 97:067202, Aug 2006.
  11. [11] A. Dorneich and M. Troyer. Accessing the dynamics of large many-particle systems using the stochastic series expansion. Phys. Rev. E, 64:066701, Nov 2001.
  12. [12] D. J. Earl and M. W. Deem. Parallel tempering: Theory, applications, and new perspectives. Phys. Chem. Chem. Phys., 7:3910–3916, 2005.
  13. [13] M. E. Fisher and A. N. Berker. Scaling for first-order phase transitions in thermodynamic and finite systems. Phys. Rev. B, 26:2507–2513, Sep 1982.
  14. [14] D. Garanin and P. Kladko, K.and Fulde. Quasiclassical Hamiltonians for large-spin systems. The European Physical Journal B - Condensed Matter and Complex Systems, 14(2):293, Mar 2000.
  15. [15] M. J. Gingras and P. A. McClarty. Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets. Reports on Progress in Physics, 77(5):056501, 2014.
  16. [16] J. Helmes, L. E. Hayward Sierens, A. Chandran, W. Witczak-Krempa, and R. G. Melko. Universal corner entanglement of dirac fermions and gapless bosons from the continuum to the lattice. Phys. Rev. B, 94:125142, Sep 2016.
  17. [17] M. Hermele, M. P. A. Fisher, and L. Balents. Pyrochlore photons: The U(1) spin liquid in a S=1/2 three-dimensional frustrated magnet. Phys. Rev. B, 69:064404, Feb 2004.
  18. [18] R. Higashinaka, H. Fukazawa, and Y. Maeno. Anisotropic release of the residual zero-point entropy in the spin ice compound Dy 2 Ti 2 O 7 : Kagome ice behavior. Phys. Rev. B, 68:014415, Jul 2003.
  19. [19] Y.-P. Huang, G. Chen, and M. Hermele. Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice. Phys. Rev. Lett., 112:167203, Apr 2014.
  20. [20] Y.-P. Huang and M. Hermele. Theory of quantum kagome ice and vison zero modes. Phys. Rev. B, 95:075130, Feb 2017.
  21. [21] S. V. Isakov, S. Wessel, R. G. Melko, K. Sengupta, and Y. B. Kim. Hard-core bosons on the kagome lattice: Valence-bond solids and their quantum melting. Phys. Rev. Lett., 97:147202, Oct 2006.
  22. [22] K. Kanô and S. Naya. Antiferromagnetism. the kagomé ising net. Progress of Theoretical Physics, 10(2):158–172, 1953.
  23. [23] A. Kitaev and J. Preskill. Topological entanglement entropy. Phys. Rev. Lett., 96:110404, Mar 2006.
  24. [24] J. Knolle and R. Moessner. A field guide to spin liquids. arXiv preprint arXiv:1804.02037, 2018.
  25. [25] S. Lee, S. Onoda, and L. Balents. Generic quantum spin ice. Phys. Rev. B, 86:104412, Sep 2012.
  26. [26] M. Levin and X.-G. Wen. Detecting topological order in a ground state wave function. Phys. Rev. Lett., 96:110405, Mar 2006.
  27. [27] E. Lhotel, S. Petit, M. C. Hatnean, J. Ollivier, H. Mutka, E. Ressouche, M. R. Lees, and G. Balakrishnan. Dynamic quantum kagome ice, 2017.
  28. [28] C.-W. Liu, A. Polkovnikov, and A. W. Sandvik. Quasi-adiabatic quantum Monte Carlo algorithm for quantum evolution in imaginary time. Phys. Rev. B, 87:174302, May 2013.
  29. [29] G.-H. Liu, R.-Y. Li, and G.-S. Tian. Quantum entanglement and criticality of the antiferromagnetic Heisenberg model in an external field. Journal of Physics: Condensed Matter, 24(25):256002, 2012.
  30. [30] R. G. Melko. Simulations of quantum XXZ models on two-dimensional frustrated lattices. Journal of Physics: Condensed Matter, 19(14):145203, 2007.
  31. [31] R. G. Melko, A. B. Kallin, and M. B. Hastings. Finite-size scaling of mutual information in monte carlo simulations: Application to the spin- 2 1 XXZ model. Phys. Rev. B, 82:100409, Sep 2010.
  32. [32] S. Miyashita and H. Kawamura. Phase transitions of anisotropic Heisenberg antiferromagnets on the triangular lattice. J. Phys. Soc. Jpn., 54:3385, 1985.
  33. [33] R. Moessner and S. L. Sondhi. Ising models of quantum frustration. Phys. Rev. B, 63:224401, May 2001.
  34. [34] T. Neupert, L. Santos, C. Chamon, and C. Mudry. Fractional quantum hall states at zero magnetic field. Phys. Rev. Lett., 106:236804, Jun 2011.
  35. [35] P. Nikolić and T. Senthil. Theory of the kagome lattice ising antiferromagnet in weak transverse fields. Phys. Rev. B, 71:024401, Jan 2005.
  36. [36] S. A. Owerre, A. A. Burkov, and R. G. Melko. Linear spin-wave study of a quantum kagome ice. Phys. Rev. B, 93:144402, Apr 2016.
  37. [37] M. Powalski, K. Coester, R. Moessner, and K. P. Schmidt. Disorder by disorder and flat bands in the kagome transverse field ising model. Phys. Rev. B, 87:054404, Feb 2013.
  38. [38] R. E. Prange and S. M. Girvin. The Quantum Hall effect. Springer-Verlag, New York, 2nd ed. edition, 1990.
  39. [39] V. Privman. Finite Size Scaling and Numerical Simulation of Statistical Systems, chapter 1, pages 1–98. World Scientific, 2014.
  40. [40] J. Rehn, A. Sen, and R. Moessner. Fractionalized Z2 classical Heisenberg spin liquids. Phys. Rev. Lett., 118:047201, Jan 2017.
  41. [41] K. A. Ross, L. Savary, B. D. Gaulin, and L. Balents. Quantum excitations in quantum spin ice. Phys. Rev. X, 1:021002, Oct 2011.
  42. [42] E. Rowell, R. Stong, and Z. Wang. On classification of modular tensor categories. Communications in Mathematical Physics, 292(2):343–389, Dec 2009.
  43. [43] A. W. Sandvik. A generalization of handscomb’s quantum monte carlo scheme application to the 1D hubbard model. Journal of Physics A: Mathematical and General, 25(13):3667, 1992.
  44. [44] A. W. Sandvik. Finite-size scaling of the ground-state parameters of the two-dimensional Heisenberg model. Phys. Rev. B, 56:11678–11690, Nov 1997.
  45. [45] L. Savary and L. Balents. Coulombic quantum liquids in spin-1/2 pyrochlores. Phys. Rev. Lett., 108:037202, Jan 2012.
  46. [46] L. Savary and L. Balents. Quantum spin liquids: a review. Reports on Progress in Physics, 80(1):016502, 2016.
  47. [47] L. Savary and L. Balents. Disorder-induced quantum spin liquid in spin ice pyrochlores. Phys. Rev. Lett., 118:087203, Feb 2017.
  48. [48] P. Sengupta, A. W. Sandvik, and D. K. Campbell. Bond-order-wave phase and quantum phase transitions in the one-dimensional extended hubbard model. Phys. Rev. B, 65:155113, Apr 2002.
  49. [49] M. B. H. . R. G. M. Sergei V. Isakov. Topological entanglement entropy of a Bose-Hubbard spin liquid. Nature, 7:772, July 2011.
  50. [50] K. Sun, Z. Gu, H. Katsura, and S. Das Sarma. Nearly flatbands with nontrivial topology. Phys. Rev. Lett., 106:236803, Jun 2011.
  51. [51] O. F. Syljuåsen and A. W. Sandvik. Quantum Monte Carlo with directed loops. Phys. Rev. E, 66:046701, Oct 2002.
  52. [52] E. Tang, J.-W. Mei, and X.-G. Wen. High-temperature fractional quantum Hall states. Phys. Rev. Lett., 106:236802, Jun 2011.
  53. [53] X.-G. Wen. Colloquium: Zoo of quantum-topological phases of matter. Rev. Mod. Phys., 89:041004, Dec 2017.
  54. [54] S. Wenzel and W. Janke. Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model. Phys. Rev. B, 78:064402, Aug 2008.
  55. [55] M.-C. Wu. Exact finite-size scaling functions for the interfacial tensions of the Ising model on planar lattices. Physical Review E, 73(4):046135, 2006.