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| Title: | 非週期性鍵結海森堡模型之重整化群研究
Renormalization group studies of Heisenberg chains with aperiodic couplings |
| Authors: | 王奕翔
Wang, Yi-Xiang |
| Contributors: | 林瑜琤
Lin, Yu-Cheng
王奕翔
Wang, Yi-Xiang |
| Keywords: | 張量網路重整化群
密度矩陣重整化群
非週期性
量子自旋鏈
Tensor network renormalization group method
Density matrix renormalization group
Aperiodicity
Quantum spin chains |
| Date: | 2023 |
| Issue Date: | 2023-09-01 16:28:07 (UTC+8) |
| Abstract: | 在海森堡（Heisenberg）反鐵磁鏈中，無序性將導致系統基態呈現出隨機單態，此為強無序重整化群法所推演出的關鍵結果。此方法的設計使之在無序系統低溫下能求得近似精確解。在本論文我們採用一強無序重整化群法的改良方法—樹狀張量網路強無序重整化群法，來探討帶有確定性但非週期耦合之自旋 1/2 鏈基態性質。非周期性效應對低溫性質的影響取決於平均耦合常數的局部波動，若非週期性屬攸關擾動，則該系統與完全無序系統會呈現出一定的相似性。若非週期性屬無關擾動，系統行為會表現如同均質情況，而屬邊際型的非週期性則可能導致非普適性的行為。藉由與密度矩陣重整化群法的結果作比較，我們檢驗了在各種類型的非週期性調變下樹狀張量網路重整化群法的效力，而這些非週期性調變在影響自旋鏈的基態性質中，可能屬攸關、邊際或無關型。
Randomness in Heisenberg antiferromagnetic chains leads to the random-singlet ground state, which is a key analytical result of the strong-disorder renormalization group (SDRG) method. This method is designed to be asymptotically exact at low energies in the presence of disorder. Here we use a tree tensor network renormalization group (RG) method, an adaptation of SDRG, to study the ground state properties of S = 1/2 spin chains with deterministic aperiodic couplings. The effects of aperiodicity on low-temperature properties depend on the local fluctuations of the mean coupling constant. If the aperiodicity is a relevant perturbation, the system may bear some similarities with completely random systems. With irrelevant aperiodicity, the system behaves as in the uniform case. Marginal aperiodicity may lead to non-universal behavior. By comparing with density matrix RG results, we examine the validity of the tree tensor RG method for various types of aperiodic modulations that are relevant, marginal, or irrelevant in affecting the ground state properties of the spin chains. |
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| Description: | 碩士
國立政治大學
應用物理研究所
110755002 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0110755002 |
| Data Type: | thesis |
| Appears in Collections: | [應用物理研究所 ] 學位論文
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