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| 题名: | 反鐵磁易辛自旋鏈在外加橫場及縱場的量子蒙地卡羅計算
Quantum Monte Carlo studies of the antiferromagnetic Ising spin chain in transverse and longitudinal fields |
| 作者: | 徐哲仁
Hsu, Zhe Ren |
| 贡献者: | 林瑜琤
Lin, Yu Cheng
徐哲仁
Hsu, Zhe Ren |
| 关键词: | 量子反鐵磁易辛自旋鏈
量子相變
臨界點
強無序
quantum antiferromagnetic Ising chain
quantum phase transition
critical point
strong disorder |
| 日期: | 2013 |
| 上传时间: | 2014-10-01 13:15:06 (UTC+8) |
| 摘要: | 磁性物質於絕對零溫時的量子相變為近代凝態物理的主要研究課題之一。在本論文中我們應用量子蒙地卡羅模擬探討橫場及縱場下之反鐵磁易辛自旋鏈的零溫相圖及其臨界現象。近鄰易辛反鐵磁性交互作用驅使系統形成 z 方向的交錯磁有序。隨著橫向磁場 h^x ---此為量子力學參數 --- 的改變，易辛自旋鏈將由具反鐵磁性的有序基態（當易辛交互作用為主宰項時）經量子相變至順磁性基態（當外加橫場主宰系統時）。加諸一沿易軸方向的磁場 h^z 能進一步削弱反鐵磁有序。我們考慮兩種類型的交互耦合：一、均質情形：自旋交互作用及加諸於各自旋的磁場均與晶格點位置無關；二、無序情形：自旋交互作用及加諸於各自旋的橫向磁場為隨機無序的。對均質系統而言，在 (h^x, h^z) 相圖平面上一臨界線區隔反鐵磁相及順磁相，該臨界線終止於 h^x = 0 處之多相臨界點，此處發生古典一階相變。數值結果得以驗證均質系統 h^x > 0 的臨界線屬二維古典易辛模型的相變普適類。而對於無序系統來說，h^z = 0 處為一具有無窮大動力學指數的非尋常量子臨界點；在有限縱場之下，我們的數值結果顯示量子相變因無序效應而變模糊不明確。
The study of quantum phase transitions in magnetic materials has been a major focus of modern condensed-matter physics. In this thesis we study the zero-temperature phase diagram and critical properties of the antiferromagnetic Ising spin chain in transverse and longitudinal magnetic fields by quantum Monte Carlo simulations. The nearest-neighbor Ising interaction favors staggered magnetic ordering along the z axis. As we vary a transverse magnetic field h^x, which is a quantum mechanical parameter, the Ising spin chain will undergo a quantum phase transition from an antiferromagnetic ordered ground state when the interaction dominates to a paramagnetic ground state when the applied transverse field dominates. A magnetic field h^z applied along the Ising axis can further destabilize antiferromagnetic order. We consider two types of couplings: (i) the homogeneous case where the interaction and the magnetic fields are site-independent; (ii) the disordered case where site-to-site variations of the interaction and the transverse field are random. For the homogeneous case, the antiferromagnetic phase and the paramagnetic phase are separated by a critical line in (h^x, h^z) plane, ending at the multicritical point with h^x=0 where a classical first-order transition occurs. It is found numerically that the critical line for h^x>0 belongs to the universality class of the two-dimensional classical Ising model. For the disordered case, the quantum critical point for h^z=0 is of unconventional infinite-randomness type with infinite dynamic exponent. In a finite longitudinal field, our numerical results suggest that the sharp global quantum phase transition is destroyed by smearing. |
| 參考文獻: | [1] P. W. Anderson, Science 177, 393 (1972).
[2] J. P. Sethna, Statistical Mechanics: Entropy, Order Parameters and Complexity,
Oxford University Press, 2006.
[3] N. D. Mermin, Phys. Rev. Lett. 26, 957 (1971).
[4] M. Le Bellac, Equilibrium and non-equilibrium statistical thermodynamics, Cambridge University Press, 2004.
[5] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, and M. P. A. Fisher, Science 303, 1490 (2004).
[6] A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007).
[7] K. G. Wilson, Phys. Rev. B 4, 3174 (1971).
[8] K. G. Wilson, Phys. Rev. B 4, 3184 (1971).
[9] S. Sachdev, Quantum Phase Transitions, Cambridge University Press, second edition, 2011, Cambridge Books Online.
[10] R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).
[11] A. R. H. Richard P. Feynman, Quantum Mechanics and Path Integrals, McGraw-Hill Companies, 1965.
[12] A. B. Harris, Journal of Physics C: Solid State Physics 7, 1671 (1974).
[13] R. B. Griffiths, Phys. Rev. Lett. 23, 17 (1969).
[14] B. M. McCoy, Phys. Rev. Lett. 23, 383 (1969).
[15] B. M. McCoy and T. T. Wu, Phys. Rev. 176, 631 (1968).
[16] M. Thill and D. Huse, Physica A: Statistical Mechanics and its Applications 214, 321 (1995).
[17] D. S. Fisher, Phys. Rev. Lett. 69, 534 (1992).
[18] D. S. Fisher, Phys. Rev. B 51, 6411 (1995).
[19] H. Rieger and A. P. Young, Phys. Rev. B 54, 3328 (1996).
[20] S. Guo et al., Phys. Rev. Lett. 100, 017209 (2008).
[21] T. Westerkamp et al., Phys. Rev. Lett. 102, 206404 (2009).
[22] S. Ubaid-Kassis, T. Vojta, and A. Schroeder, Phys. Rev. Lett. 104, 066402 (2010).
[23] C. Pich, A. P. Young, H. Rieger, and N. Kawashima, Phys. Rev. Lett. 81, 5916 (1998).
[24] O. Motrunich, S.-C. Mau, D. A. Huse, and D. S. Fisher, Phys. Rev. B 61, 1160 (2000).
[25] Y.-C. Lin, F. Iglói, and H. Rieger, Phys. Rev. Lett. 99, 147202 (2007).
[26] I. A. Kovács and F. Iglói, Journal of Physics: Condensed Matter 23, 404204 (2011).
[27] D. Bitko, T. F. Rosenbaum, and G. Aeppli, Phys. Rev. Lett. 77, 940 (1996).
[28] H. M. Rønnow et al., arXiv preprint cond-mat/0505064 (2005).
[29] H. M. Rønnow et al., Science 308, 389 (2005).
[30] P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928).
[31] P. Pfeuty, Annals of Physics 57, 79 (1970).
[32] C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (1952).
[33] T. D. Lee and C. N. Yang, Phys. Rev. 87, 410 (1952).
[34] R.Dobrushin, J. Kolafa, and S.Shlosman, Communications in Mathematical Physics 102, 89 (1985).
[35] X. Wu and F. Wu, Physics Letters A 144, 123 (1990).
[36] P. Sen, Phys. Rev. E 63, 016112 (2000).
[37] A. A. Ovchinnikov, D. V. Dmitriev, V. Y. Krivnov, and V. O. Cheranovskii, Phys. Rev. B 68, 214406 (2003).
[38] S. K. Niesen et al., Phys. Rev. B 87, 224413 (2013).
[39] S. Kimura et al., Journal of Physics: Conference Series 51, 99 (2006).
[40] J. Simon et al., Nature 472, 307 (2011).
[41] M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature 415, 39 (2002).
[42] M. P. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Phys. Rev. B 40, 546 (1989).
[43] D. Jaksch, C. Bruder, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).
[44] S. Sachdev, K. Sengupta, and S. Girvin, Phys. Rev. B 66, 075128 (2002).
[45] J. Simon et al., arXiv preprint 1103.1372 (2011).
[46] H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959).
[47] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
[48] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
[49] M. P. Nightingale and H. W. J. Blöte, Phys. Rev. B 62, 1089 (2000).
[50] K. Hukushima and K. Nemoto, Journal of the Physical Society of Japan 65, 1604 (1996).
[51] D. J. Earl and M. W. Deem, Phys. Chem. Chem. Phys. 7, 3910 (2005).
[52] V.Privman, Finite-size scaling theory, volume1, Singapore: World Scientific, 1990.
[53] J. Cardy, Scaling and Renormalization in Statistical Physics, Cambridge University Press, 1996.
[54] K. Binder, Phys. Rev. Lett. 47, 693 (1981).
[55] K. Binder, Zeitschrift für Physik B Condensed Matter 43, 119 (1981).
[56] L. Onsager, Phys. Rev. 65, 117 (1944).
[57] V. S. Dotsenko and V. S. Dotsenko, Advances in Physics 32, 129 (1983).
[58] B. Shalaev, Physics Reports 237, 129 (1994).
[59] R. Shankar and G. Murthy, Phys. Rev. B 36, 536 (1987).
[60] M. Guo, R. N. Bhatt, and D. A. Huse, Phys. Rev. Lett. 72, 4137 (1994).
[61] H. Rieger and A. P. Young, Phys. Rev. Lett. 72, 4141 (1994).
[62] P. Pfeuty, Phys. Lett. A 72, 245 (1979).
[63] E. Lieb, T. Schultz, and D. Mattis, Annals of Physics 16, 407 (1961).
[64] T. Vojta, Phys. Rev. Lett. 90, 107202 (2003).
[65] T. Vojta, Journal of Physics A: Mathematical and General 39, R143 (2006). [66] H. Rieger and N. Kawashima, Eur. Phys. J. B 9, 233 (1900).
[67] A. W. Sandvik, Phys. Rev. E 68, 056701 (2003). |
| 描述: | 碩士
國立政治大學
應用物理研究所
100755004
102 |
| 資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0100755004 |
| 数据类型: | thesis |
| 显示于类别: | [應用物理研究所 ] 學位論文
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