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| 研究生： |
張鎮宇 Chang, Chen Yu |
|---|---|
| 論文名稱： |
三角晶格易辛反鐵磁之量子相變 Quantum phase transition in the triangular lattice Ising antiferromagnet |
| 指導教授： |
林瑜琤
Lin, Yu Cheng |
| 口試委員: |
陳柏中
林瑜琤 楊志開 張明哲 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用物理研究所 Graduate Institute of Applied Physics |
| 論文出版年： | 2017 |
| 畢業學年度： | 105 |
| 語文別： | 中文 |
| 論文頁數： | 37 |
| 中文關鍵詞： | 挫折性反鐵磁 、零溫投射蒙地卡羅演算法 、隨機序列展開演算法 、絕熱量子模擬 、模擬退火 、動力學指數 |
| 外文關鍵詞： | Frustrated antiferromagnet, Zero-temperature projector algorithm, Stochastic series expansion, Adiabatic quantum simulation, Simulated annealing, Dynamical exponent |
| 相關次數： | 點閱：107 下載：56 |
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量子擾動及挫折性兩者均可破壞絕對零溫的磁序，為近代凝態物 理關注的有趣現象。在外加橫場下的三角晶格易辛反鐵磁兼具量子臨 界現象(quantum criticality)及幾何挫折性，可謂量子磁性物質之一典 範理論模型。本論文利用平衡態及非平衡態量子蒙地卡羅(quantum Monte Carlo)方法探測三角晶格易辛反鐵磁之量子相變，其界定零溫 時無磁性的順磁態及具 Z6 對稱破缺的有序態(所謂時鐘態)。這裡的 量子蒙地卡羅方法為運用算符的零溫投射(zero-temperature projector) 及隨機序列展開(stochastic series expansion)演算法。在非平衡模擬 中，我們分別沿降溫過程及量子絕熱過程逼近量子相變點，藉此我們 得到動力學指數，及其它相關臨界指數。
The destruction of magnetic long-range order at absolute zero temperature arising from quantum fluctuations and frustration is an interesting theme in modern condensed-matter physics. The triangular lattice Ising antiferromag- net in a transverse field provides a playground for the study of the combined effects of quantum criticality and geometrical frustration. In this thesis we use quantum Monte Carlo methods both in equilibrium and non-equilibrium setups to study the properties of the quantum critical point in the triangular lattice antiferromagnet, which separates a disordered paramagnetic state and an ordered clock state exhibiting Z6 symmetry breaking; The methods are based on a zero-temperature projector algorithm and the stochastic series ex- pansion algorithm. For the non-equilibrium setups, we obtain the dynamical exponent and other critical exponents at the quantum critical point approached by slowly decreasing temperature and through quantum annealing.
摘要 i
Abstract iii
目錄 v
1 三角量子易辛反鐵磁 1
2 零溫投射量子蒙地卡羅法 5
2.1 零溫投射法之基本概念 5
2.2 處理量子易辛模型的零溫投射法 7
2.2.1 局域組態更新法則 9
2.2.2 叢集更新法則 11
2.3 零溫標度分析 11
2.4 量子絕熱演化 15
3 隨機級數展開量子蒙地卡羅方法 23
3.1 量子易辛模型的隨機級數展開法 23
3.2 有限溫度下的平衡態模擬 26
3.3 模擬退火 30
4 總結與展望 33
參考文獻 33
[1] G. H. Wannier, Phys. Rev. 79, 357 (1950).
[2] J. Stephenson, Journal of Mathematical Physics 11, 413 (1970).
[3] Y. Jiang and T. Emig, Phys. Rev. B 73, 104452 (2006).
[4] R. Moessner, S. L. Sondhi, and P. Chandra, Phys. Rev. Lett. 84, 4457 (2000).
[5] R. Moessner and S. L. Sondhi, Phys. Rev. B 63, 224401 (2001).
[6] R. Moessner, S. L. Sondhi, and P. Chandra, Phys. Rev. B 64, 144416 (2001).
[7] S. V. Isakov and R. Moessner, Phys. Rev. B 68, 104409 (2003).
[8] D. Blankschtein, M. Ma, A. N. Berker, G. S. Grest, and C. M. Soukoulis, Phys. Rev. B 29, 5250 (1984).
[9] H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959).
[10] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976).
[11] J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, Phys. Rev. B 16, 1217 (1977).
[12] D. R. Nelson and J. M. Kosterlitz, Phys. Rev. Lett. 39, 1201 (1977).
[13] J. Cardy, Scaling and renormalization in statistical physics, volume 5, Cambridge university press, 1996.
[14] M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev. B 63, 214503 (2001).
[15] M. Žukovič, L. Mižišin, and A. Bobák, Acta Physica Polonica A 126, 40 (2014).
[16] S. Liang, Phys. Rev. B 42, 6555 (1990).
[17] A. W. Sandvik, Phys. Rev. Lett. 95, 207203 (2005).
[18] A. W. Sandvik and K. S. D. Beach, arXiv:0704.1469, (2007).
[19] R. G. Melko, Stochastic Series Expansion Quantum Monte Carlo, pages 185–206, Springer Berlin Heidelberg, Berlin, Heidelberg, 2013.
[20] A. W. Sandvik, Phys. Rev. E 68, 056701 (2003).
[21] S. Inglis and R. G. Melko, New Journal of Physics 15, 073048 (2013).
[22] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953).
[23] R. H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 58, 86 (1987).
[24] K. Binder, Phys. Rev. Lett. 47, 693 (1981).
[25] A. W. Sandvik, AIP Conf. Proc. 1297, 135 (2010).
[26] E. Farhi et al., Science 292, 472 (2001).
[27] C.-W. Liu, A. Polkovnikov, and A. W. Sandvik, Phys. Rev. B 87, 174302 (2013).
[28] C.-W.Liu,A.Polkovnikov,andA.W.Sandvik,Phys.Rev.Lett.114,147203(2015).
[29] M. W. Johnson et al., Nature 473, 194 (2011).
[30] M. Born and V. Fock, Zeitschrift fur Physik 51, 165 (1928).
[31] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998).
[32] G. E. Santoro, R. Martoňák, E. Tosatti, and R. Car, Science 295, 2427 (2002).
[33] G. E. Santoro and E. Tosatti, Journal of Physics A: Mathematical and General 39, R393 (2006).
[34] S. Boixo et al., Nature Physics 10, 218 (2014).
[35] C. De Grandi and A. Polkovnikov, Adiabatic Perturbation Theory: From Landau– Zener Problem to Quenching Through a Quantum Critical Point, pages 75–114, Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.
[36] 黃湘喻, 以模擬量子退火過程探索自旋系統的基態, Master’s thesis, 國立政治 大學, 2014.
[37] B. Damski and W. H. Zurek, Phys. Rev. A 73, 063405 (2006).
[38] T. W. Kibble, Journal of Physics A: Mathematical and General 9, 1387 (1976).
[39] T. W. Kibble, Physics Reports 67, 183 (1980).
[40] W. Zurek, Nature 317, 505 (1985).
[41] W. H. Zurek, Physics Reports 276, 177 (1996).
[42] J. Dziarmaga, Phys. Rev. Lett. 95, 245701 (2005).
[43] A. Polkovnikov, Phys. Rev. B 72, 161201 (2005).
[44] W. H. Zurek, U. Dorner, and P. Zoller, Phys. Rev. Lett. 95, 105701 (2005).
[45] A. W. Sandvik and J. Kurkijärvi, Phys. Rev. B 43, 5950 (1991).
[46] A. W. Sandvik, Journal of Physics A: Mathematical and General 25, 3667 (1992).
[47] D. C. Handscomb, Mathematical Proceedings of the Cambridge Philosophical So- ciety 58, 594–598 (1962).
[48] D. C. Handscomb, Mathematical Proceedings of the Cambridge Philosophical So- ciety 60, 115–122 (1964).
[49] A. W. Sandvik, Phys. Rev. B 56, 11678 (1997).
[50] M. Hasenbusch and S. Meyer, Physics Letters B 241, 238 (1990).
