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    Title: 關於量子蒙地卡羅退火法
    On quantum Monte Carlo annealing
    Authors: 何政緯
    Ho, Zheng-Wei
    Contributors: 林瑜琤
    Lin, Yu-Cheng
    何政緯
    Ho, Zheng-Wei
    Keywords: 模擬退火
    隨機級數展開量子蒙地卡羅演算法
    零溫投射蒙地卡羅演算法
    非均質量子易辛鏈
    三角反鐵磁
    Kosterlitz-Thouless 相變
    simulated annealing
    stochastic series expansion method
    zero-temperature projector method
    random quantum Ising chain
    triangular Ising antiferromagnet
    Kosterlitz-Thouless transition
    Date: 2019
    Issue Date: 2019-09-05 16:15:50 (UTC+8)
    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。
    This 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.
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    Description: 碩士
    國立政治大學
    應用物理研究所
    106755006
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G1067550061
    Data Type: thesis
    DOI: 10.6814/NCCU201901066
    Appears in Collections:[應用物理研究所 ] 學位論文

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