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 |
相關次數: | 點閱:1 下載:0 |
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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
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