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研究生: 劉少輔
Liu, Shao-Fu
論文名稱: 一維bond-alternating無序海森堡鏈之重整化群分析
Study of 1-dimensional bond-alternating Heisenberg spin chain by tSDRG
指導教授: 陳柏中
Chen, Po-Chung
口試委員: 林瑜琤
Lin, Yu-Cheng
黃一平
Huang, Yi-Ping
學位類別: 碩士
Master
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2022
畢業學年度: 110
語文別: 英文
論文頁數: 47
中文關鍵詞: 強無序重整化群無序海森堡鏈張量網路
外文關鍵詞: strong disorder renormalization group, bond-alternating random Heisenberg chain, tensor network
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  • 本篇論文中,我們利用樹狀張量網路強無序重整化群的數值方法對一維S=1與S=2 bond-alternating海森堡鏈分析。首先我們介紹了twist order parameter ZL以及VBS態分析,並計算在不同無序強度R及bond alternation強度δ下的ZL,利用有限長度擬合方法找出對應的相變點以及在(R,δ)平面的相圖。
    對於S=1,我們的結果與其他現有數值模擬計算的結果大致相符。
    對於S=2,我們利用S=1的方法來分析,並將以上結果進行總結,我們在現有理論預測的兩種相圖中,給出最有可能的其中一種相圖。


    In this thesis, we use a tree tensor network strong disorder renormalization group method to study spin-1 and spin-2 bond-alternating antiferromagnetic Heisenberg chain (BAHC). First, we introduce the twist order parameter ZL and VBS picture, by calculating ZL under different strengths of disorder R and bond alternation δ, we could use finite size scaling to find out the corresponding phase transition points and the phase diagram in the (R,δ) plane.
    For S=1, our results are in a good agreement with existing result
    obtained by other numerical methods.
    For S=2, there are currently two possible theoretical phase diagrams, by using the same analysis methods in spin-1 case, we summarize our results to give a conjecture that the phase diagram should belong to one of them

    Contents Abstract (Chinese) 1 Acknowledgements (Chinese) 2 Abstract 3 Contents 4 1 Introduction 6 1.1 Disorder system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 1-D bond-alternating Heisenberg model . . . . . . . . . . . . . . . . 7 1.3 VBS states and Twist order parameter . . . . . . . . . . . . . . . . 8 2 Numerical analysis 10 2.1 Matrix Product Operator . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Tree tensor network strong disorder renormalization group . . . . . 13 3 Spin 1 Result 18 3.1 Prediction for spin-1 phase diagram . . . . . . . . . . . . . . . . . . 18 3.2 Finite size scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Compare the result . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Spin 2 Result 29 4.1 Prediction of spin-2 phase diagram . . . . . . . . . . . . . . . . . . 29 4.2 Finite size scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.3 Compare the result . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5 Conclusion 43 Bibliography 45

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