政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/116779

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/116779

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政大典藏 > College of Science > Graduate Institute of Applied Physics > Theses > Item 140.119/116779

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/116779

Title:	三角晶格易辛反鐵磁之量子相變 Quantum phase transition in the triangular lattice Ising antiferromagnet
Authors:	張鎮宇 Chang, Chen Yu
Contributors:	林瑜琤 Lin, Yu Cheng 張鎮宇 Chang, Chen Yu
Keywords:	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 Frustrated antiferromagnet Zero-temperature projector algorithm Stochastic series expansion Adiabatic quantum simulation Simulated annealing Dynamical exponent
Date:	2017
Issue Date:	2018-04-09 15:51:34 (UTC+8)
Abstract:	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.
Reference:	[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).
Description:	碩士國立政治大學應用物理研究所 102755004
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0102755004
Data Type:	thesis
Appears in Collections:	[Graduate Institute of Applied Physics] Theses

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