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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲(Ying-Jer Kao) | |
| dc.contributor.author | Jun-Gu Chen | en |
| dc.contributor.author | 陳俊谷 | zh_TW |
| dc.date.accessioned | 2021-06-12T17:57:45Z | - |
| dc.date.available | 2008-02-18 | |
| dc.date.copyright | 2008-02-18 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-01-30 | |
| dc.identifier.citation | [1] J. M. Hopkinson, S. V. Isakov, H.-Y. Kee, and Y. B. Kim, Phys. Rev. Lett. 99, 037207 (2007).
[2] J. Schnack, H.-J. Schmidt, A. Honecker, J. Schulenburg, and J. Richter, J. Phys.: Conf. Ser. 51, 43 (2006). [3] D. Dai and M.-H. Whangbo, J. Chem. Phys. 121, 672 (2004). [4] R. Moessner, Can. J. Phys. 79, 1283 (2001). [5] Y. Okamoto, M. Nohara, H. Aruga-Katori, and H. Takagi, Phys. Rev. Lett. 99, 137207 (2007). [6] J. Schulenburg, A. Honecker, J. Schnack, J. Richter1, and H.-J. Schmidt, Phys. Rev. Lett. 88, 167207 (2002). [7] D. C. Mattis, THE THEORY OF MAGNETISM MADE SIMPLE (World Scientific, Singapore, 2006). [8] J. Richter, J. Schulenburg, A. Honecker, J. Schnack, and H.-J. Schmidt, J. Phys.: Condens. Matter 16, S779 (2004). [9] T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, INTRODUCTION TO ALGORITHMS, second ed. (The MIT Press, 2001). [10] A. Honecker and J. Richter, Condensed Matter Physics 8, 813 (2005). [11] C. Kittel, Introduction to Solid State Physics, seventh ed. (Wiley, New York, USA, 1984). [12] N. W. Ashcroft and N. D. Mermin, Solid State Physics (Thomson Leaning,1976). [13] F. Anfuso and S. Eggert, Phys. Rev. Lett. 96, 017204 (2006). [14] J.Schnack and M. Luban, Phys. Rev. B 63, 014418 (2000). [15] J. Schnack, H.-J. Schmidt, J. Richter, and J. Schulenburg, Eur. Phys. J. B 24, 475 (2001). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27199 | - |
| dc.description.abstract | 我們發展了一個研究多體物理的數值方法叫做精確對角化(Exact
Diagonalization, ED)。這個方法可經由對角化漢彌爾(Hamiltonian)來計算各種物理觀測值。在第二章中我們將詳述這個方法的原理及實行。而在第三章中，我們將用精確對角化這個方法去探究先前在二維六邊形晶格上的一些奇異現象，如磁化跳躍。及用以解釋磁化跳躍這個不尋常現象的想法叫做局域磁子狀態(Localized Magnon State, LMS)。第四章我們將用精確對角化的方法去研究三維類六邊形晶格的基本性質，及探索是否也存在有磁化跳躍這樣的情形。 | zh_TW |
| dc.description.abstract | We develop a numerical method which is called exact diagonalization(ED) in our group. The method can exactly calculate various physical observables by diagonalizing the Hamiltonian. The ED methods will be discussed in Chap2.
In Chap.3, we will perform some calculations such as the knight shift around single impurity in square lattice. And the properties of the kagome lattice such as magnetization to check our codes. We will also use ED method to caculate some properties of the hyperkagome lattice in Chap.4. We find some anomalous phenomena and some good properties in the hyperkagome lattice such as magnetization jump and the adiabatic demagnetization curve. We try to explain these phenomena by the localized magnon states which will be introduced in Sec.1.4. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-12T17:57:45Z (GMT). No. of bitstreams: 1 ntu-97-R94222064-1.pdf: 1387693 bytes, checksum: 9b96b9614aab98fdd77aa7ac94ff2599 (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | 1 Introduction 5
1.1 Hyperkagome . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Heisenberg model . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Magnetization jump . . . . . . . . . . . . . . . . . . . . . . . 10 1.4 Localized magnon states(LMS) . . . . . . . . . . . . . . . . . 12 2 Exact Diagonalization 15 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.1 The challenge in ED . . . . . . . . . . . . . . . . . . . 16 2.1.2 Exact Diagonalization and other methods . . . . . . . 17 2.2 Practical ED procedure . . . . . . . . . . . . . . . . . . . . . . 18 2.2.1 Coding of the basis . . . . . . . . . . . . . . . . . . . 18 2.2.2 Symmetries . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.3 Finding the nonzero matrix elements . . . . . . . . . . 22 2.2.4 Full diagonalization . . . . . . . . . . . . . . . . . . . . 24 2.2.5 Lanczos Algorithm . . . . . . . . . . . . . . . . . . . . 24 2.3 A simple example . . . . . . . . . . . . . . . . . . . . . . . . . 28 3 Kagome lattice and single impurity in square lattice 32 3.1 Kagome lattice . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.2 Impurity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 Hyperkagome 41 4.1 Numerical results for the hyperkagome lattice . . . . . . . . . 43 4.2 The magnetization jump and magnon bands . . . . . . . . . . 51 5 Conclusions 60 Bibliography 62 A The code of ED 64 | |
| dc.language.iso | en | |
| dc.subject | 局域磁子態 | zh_TW |
| dc.subject | 精確對角化 | zh_TW |
| dc.subject | 六邊形晶格 | zh_TW |
| dc.subject | 三維類六邊形晶格 | zh_TW |
| dc.subject | 磁化跳躍 | zh_TW |
| dc.subject | Kagome Lattice | en |
| dc.subject | Localized Magnon State | en |
| dc.subject | Magnetization Jumps | en |
| dc.subject | Hyperkagome Lattice | en |
| dc.subject | Knight Shift | en |
| dc.subject | Exact Diagonalization | en |
| dc.title | 三維類六邊形晶格的數值研究及磁化跳躍 | zh_TW |
| dc.title | A Numerical Study of Hyperkagome Lattice and Magnetization Jumps | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 胡崇德(Chong-Der Hu),郭光宇(Guang-Yu Guo) | |
| dc.subject.keyword | 精確對角化,六邊形晶格,三維類六邊形晶格,磁化跳躍,局域磁子態, | zh_TW |
| dc.subject.keyword | Exact Diagonalization,Kagome Lattice,Knight Shift,Hyperkagome Lattice,Magnetization Jumps,Localized Magnon State, | en |
| dc.relation.page | 77 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-01-30 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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