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研究生:張鎮宇
研究生(外文):Chang, Chen Yu
論文名稱:三角晶格易辛反鐵磁之量子相變
論文名稱(外文):Quantum phase transition in the triangular lattice Ising antiferromagnet
指導教授:林瑜琤
指導教授(外文):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
校院名稱:國立政治大學
系所名稱:應用物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
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 antiferromagnetZero-temperature projector algorithmStochastic series expansionAdiabatic quantum simulationSimulated annealingDynamical exponent
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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.
目錄
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
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