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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/125647
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dc.contributor.advisor林瑜琤zh_TW
dc.contributor.advisorLin, Yu-Chengen_US
dc.contributor.author何政緯zh_TW
dc.contributor.authorHo, Zheng-Weien_US
dc.creator何政緯zh_TW
dc.creatorHo, Zheng-Weien_US
dc.date2019en_US
dc.date.accessioned2019-09-05T08:15:50Z-
dc.date.available2019-09-05T08:15:50Z-
dc.date.issued2019-09-05T08:15:50Z-
dc.identifierG1067550061en_US
dc.identifier.urihttp://nccur.lib.nccu.edu.tw/handle/140.119/125647-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用物理研究所zh_TW
dc.description106755006zh_TW
dc.description.abstract本論文檢驗以蒙地卡羅模擬退火來探討平衡態相變點定標分析之可能性。以量子易辛模型為例，我們分別探討動力學指數為 z = 1 的量子臨界點，具 z = ∞ 的無序量子臨界點，及 Kosterlitz-Thouless (KT) 相變。應用有限溫度隨機級數展開法及基態投射演算法，我們考慮的退火路徑涵蓋降溫、降橫場（量子擾動項）及同時降溫及降場三種情形。我們的計算結果顯示對於 z = 1 量子臨界點，上述後兩類量子退火過程在緩慢改變參數下均能正確反應臨界點位置及臨界指數。通過 KT 相變的退火過程亦可找出吻合理論的定標行為。唯 z = ∞ 的量子臨界點為退火過程的瓶頸，似乎任意緩慢的退火速率均很難突破這個瓶頸來達到無序系統近似靜態的極限。zh_TW
dc.description.abstractThis thesis examines the use of quantum Monte Carlo simulated annealing in the study of finite-size scaling for equilibrium phase transitions. For quantum Ising models, we study quantum critical points with the dynamic exponent z = 1, a disordered quantum critical point with z = ∞, and the Kosterlitz-Thouless (KT) transition approached through various annealing protocols in quantum Monte Carlo simulations using the stochastic series expansion method and a zero-temperature projector method. We demonstrate that annealing by decreasing a transverse field at zero temperature, or by decreasing the temperature and the transverse field simultaneously can correctly capture the critical scaling behaviors at z = 1 quantum critical points and the KT transition, if the rate of change is sufficiently slow. However, the z = ∞ quantum critical point is an annealing bottleneck and our approaches fail to reach the quasi-static limit of the random quantum Ising chain.en_US
dc.description.tableofcontents致謝 i\n摘要 iii\nAbstract v\nContents vii\n1 模型概述 1\n1.1 量子相變 1\n1.2 量子易辛模型 2\n1.3 有限尺度定標 4\n1.4 無序效應 7\n2 隨機級數展開量子蒙地卡羅方法 11\n2.1 隨機級數展開法之推導 11\n2.1.1 局域更新 15\n2.1.2 叢集更新 19\n2.2 無序系統的SSE方法 20\n2.3 零溫投射量子蒙地卡羅方法 22\n2.3.1 基態投射法 23\n3 模擬結果 27\n3.1 自旋鐵磁鏈及方晶格鐵磁 27\n3.1.1 平衡態模擬 27\n3.1.2 模擬退火與Kibble-Zurek機制 30\n3.1.3 模擬退火 34\n3.1.4 零溫模擬退火 46\n3.2 三角反鐵磁 47\n3.3 無序自旋鏈 52\n3.3.1 有限溫度模擬退火 52\n3.3.2 零溫模擬退火 57\n4 結論 61\n參考文獻 63zh_TW
dc.format.extent10790799 bytes-
dc.format.mimetypeapplication/pdf-
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G1067550061en_US
dc.subject模擬退火zh_TW
dc.subject隨機級數展開量子蒙地卡羅演算法zh_TW
dc.subject零溫投射蒙地卡羅演算法zh_TW
dc.subject非均質量子易辛鏈zh_TW
dc.subject三角反鐵磁zh_TW
dc.subjectKosterlitz-Thouless 相變zh_TW
dc.subjectsimulated annealingen_US
dc.subjectstochastic series expansion methoden_US
dc.subjectzero-temperature projector methoden_US
dc.subjectrandom quantum Ising chainen_US
dc.subjecttriangular Ising antiferromagneten_US
dc.subjectKosterlitz-Thouless transitionen_US
dc.title關於量子蒙地卡羅退火法zh_TW
dc.titleOn quantum Monte Carlo annealingen_US
dc.typethesisen_US
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dc.identifier.doi10.6814/NCCU201901066en_US
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