政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/131638

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/131638

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题名:	機器學習識別古典及量子自旋模型相態 Identifying phases of classical and quantum spin models with machine learning
作者:	林恆毅 Lin, Heng-Yi
贡献者:	林瑜琤 Lin, Yu-Cheng 林恆毅 Lin, Heng-Yi
关键词:	深度學習多層感知器捲積神經網路三角量子反鐵磁二維古典易辛模型 deep learning multilayer perceptron convolutional neural network triangular quantum Ising antiferromagnet two-dimensional classical Ising model
日期:	2020
上传时间:	2020-09-02 12:17:00 (UTC+8)
摘要:	三角易辛（Ising）反鐵磁在絕對零度因幾何挫折性而不具磁性。有趣的是，具量子效應的橫向磁場可誘發易辛反鐵磁零溫基態之有序性，產生具Z6 對稱破缺的時鐘態；這個零溫有序態可由更強的橫向磁場或有限溫度破壞。在絕對零度，一量子臨界點區分弱場下的有序時鐘態與強場下的無序順磁態。而在有限溫度，一Kosterlitz-Thouless相態區隔了低溫的時鐘態及高溫的順磁態。我們以量子蒙地卡羅方法針對許多不同溫度值及橫場值產生自旋組態，接著藉機器學習技術的多層感知器和捲積神經網路訓練機器辨識自旋組態與相態的關係，再以更多的自旋組態使神經網路識別其對應的相態。上述機器學習方法可頗精確辨識古典易辛模型的簡單相態，但對我們主要考慮的三角反鐵磁相態卻無法呈現良好的辨識力。 The triangular Ising antiferromagnet has no magnetic order down to zero temperature due to geometrical frustration. Interestingly, a weak transverse ﬁeld, introducing quantum fluctuations, can induce magnetic order in the triangular antiferromagnet at zero temperature, resulting in the clock phase with a broken Z6 symmetry; this ordered clock phase can be destroyed by a strong transverse ﬁeld or at finite temperature. At T=0, there is a quantum critical point separating the clock phase in weak fields and a paramagnetic phase in strong fields; at finite temperature, the antiferromagnet exhibits an extended Kosterlitz-Thouless (KT) phase intervening between the clock and paramagnetic phases. We generate spin configurations of the triangular antiferromagnet at different temperatures and transverse ﬁelds by quantum Monte Carlo (QMC) simulations. We attempt to use supervised machine learning techniques via multilayer perceptrons and convolutional neural networks to classify the phases of the antiferromagnetic system, solely based on spin configurations sampled with QMC. We find that the neural network models perform the classification task with a 70% accuracy for the triangular quantum antiferromagnet, while successfully distinguishing the classical Ising states with more than 90% accuracy.
參考文獻:	[1] G. H. Wannier, Phys. Rev. 79, 357 (1950). [2] Y. Jiang and T. Emig, Phys. Rev. B 73,104452 (2006). [3] S. V. Isakov and R. Moessner, Physical Review B 68 (2003). [4] M. Žukovič, L. Mižišin, and A. Bobák, Acta Physica Polonica A 126, 40 (2014). [5] 張鎮宇, 三角晶格易辛反鐵磁之量子相變, Master’s thesis, 國立政治大學, 2017. [6] A. W. Sandvik and J. Kurkijärvi, Phys. Rev. B 43, 5950 (1991). [7] R. G. Melko, Stochastic Series Expansion Quantum Monte Carlo, pages 185– 206, Springer, Berlin, Heidelberg, 2013. [8] G. Carleo et al., Rev. Mod. Phys. 91, 045002 (2019). [9] P. Mehta et al., Physics Reports 810, 1 (2019). [10] TensorFlow, https://www.tensorflow.org/. [11] Keras, https://keras.io/. [12] L. Bottou, Stochastic gradient descent tricks, in Neural networks: Tricks of the trade, pages 421–436, Springer, 2012. [13] D. P. Kingma and J. Ba, arXiv: 1412.6980 (2014). [14] D. E. Rumelhart and D. Zipser, Cognitive science 9, 75 (1985). 31 [15] M. A. Nielsen, Neural networks and deep learning, Determination press San Francisco, CA, 2015. [16] N. Srivastava, G. Hinton, A. Krizhevsky, I. Sutskever, and R. Salakhutdinov, J. Mach. Learn. Res. 15, 1929 (2014). [17] S. Ioffe and C. Szegedy, Batch normalization: Accelerating deep network training by reducing internal covariate shift, in Proceedings of the 32nd International Conference on International Conference on Machine Learning - Volume 37, ICML’15, page 448, JMLR.org, 2015. [18] S. Santurkar, D. Tsipras, A. Ilyas, and A. Mądry, How does batch normalization help optimization?, in Proceedings of the 32nd International Conference on Neural Information Processing Systems, NIPS’18, page 2488, Red Hook, NY, USA, 2018, Curran Associates Inc. [19] P. Mehta and D. J. Schwab, arXiv 1410.3831 (2014). [20] DeepLearning series: Convolutional Neural Networks, https://mc.ai/deeplearningseriesconvolutionalneuralnetworks/.
描述:	碩士國立政治大學應用物理研究所 106755007
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0106755007
数据类型:	thesis
DOI:	10.6814/NCCU202001705
显示于类别:	[應用物理研究所 ] 學位論文

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