臺灣博碩士論文加值系統

在這裡我們驗證了VMPS和iTEBD的可行性，雖然這裡只用了海森堡模型和易辛模型當一個簡單的研究，但是在其他的一維模型應該也要是可行的，可能會需要再增加一些物理性質進去。這邊介紹了如何在程式中使用VMPS和iTEBD演算法，這些是一種較新的數值方法，還有地方是可以改進而且繼續發展下去的。在模型中的計算中我們除了可以看到無窮長的易辛模型的基態結果與前人用手算的結果一樣外，也可以看到自旋-1/2的反鐵磁海森堡模型在到達足夠長時真的是沒有能隙的。

In this thesis, we study the one-dimensional systems using variational matrix product state (VMPS) and imaginary-time evolution block decimation methods. As two examples, only Heisenberg and transversal Ising models are calculated, however, we can see the methods to other one-dimensional models. We therefore introduce the procedures and the insights of VMPS and iTEBD. As a result, we compare the numerical results with the analytical ones, and confirm that the spin-1/2 antiferromagnetic Heisenberg model is gapless, as reported in the literature.

誌謝..................................................i
摘要..................................................ii
ABSTRACT..............................................iii
目次..................................................iv
圖目次.................................................v
1. 簡介...............................................1
2. 海森堡模型(Heisenberg Model)與易辛模型(Ising Model)..2
2.1. XXX model........................................2
2.2. Ising model in a transverse field................2
3. 矩陣乘積態(MPS, Matrix Product State)...............3
3.1. VMPS(Variational MPS)............................5
3.2. 使用python實做VMPS................................8
3.3. iTEBD(imaginary-Time-evolution Block Decimation).17
3.4. 使用python實作iTEBD...............................19
4. 結果與討論..........................................22
5. 結論...............................................28
參考文獻................................................29

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