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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲(Ying-Jer Kao) | |
| dc.contributor.author | Cheng-Wei Liu | en |
| dc.contributor.author | 劉承瑋 | zh_TW |
| dc.date.accessioned | 2021-06-13T15:40:06Z | - |
| dc.date.available | 2008-07-23 | |
| dc.date.copyright | 2008-07-23 | |
| dc.date.issued | 2008 | |
| dc.date.submitted | 2008-07-08 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/37715 | - |
| dc.description.abstract | We use the Stochastic Series Expansion Quantum Monte Carlo (SSE QMC) method [1, 2, 3] to study the impurity problem in the CuO2 plane of high-Tc superconducting materials. This plane is a 2D antiferromagnetic square lattice, at which the superconductivity usually occurs. Doping nonmagnetic impurities to replace Cu ions in this plane exhibits very strong electronic behavior. Hence the impurity problem forms an important class of strongly correlated electron systems.
In the presence of impurities in the CuO2 plane, from previous study [4], people already know that there are staggered moments localized around impurity sites. If the impurity concentration increases, both the theoretical and numerical studies [5, 6, 7] suggested that, at some critical density, there is a vanishing staggered magnetization, which is a suitable order parameter in this antiferromagnetic system. However, there is a discrepancy between the theoretical prediction and the experimental results [8] at high impurity concentration. The numerical and theoretical results are slightly higher than the experimental one. The discrepancy mentioned above leads us to consider the impurity-induced frustration interaction [9, 10] in the system. Since frustration will further destroy the order of the system, this frustrated interaction may account for this discrepancy. In this thesis, numerical results for the staggered magnetization and the Knight shifts are presented. In the final part we show numerical results that support our suggestion that frustrations will further destroy the order of a system. Also, SSE QMC faces the notorious “sign problem” [11, 12] when dealing with frustrated systems, so the numerical results about the sign problem are also briefly discussed. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T15:40:06Z (GMT). No. of bitstreams: 1 ntu-97-R95222065-1.pdf: 1054334 bytes, checksum: e80d5ae8d6a3a9fd7c9554fe421e5bbf (MD5) Previous issue date: 2008 | en |
| dc.description.tableofcontents | 1 Introduction. . . . . . . . . . . . . . . . . . . . . 7
1.1 CuO2 planes of the high-Tc cuprate . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Doping nonmagnetic impurities in the CuO2 plane . . . . . . . . . . . . . . . 8 1.3 Frustrations in the lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Lattice model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2 Numerical methods. . . . . . . . . . . . . . . . . . . . . 13 2.1 Introduction to Monte Carlo simulations . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Stochastic Series Expansion formalism . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Stochastic Series Expansion configuration space . . . . . . . . . . . . . . . . 18 2.4 Updating schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.4.1 Diagonal update . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4.2 Directed loop update . . . . . . . . .. . . . . . . . . . . . . . . . . . . 21 2.5 SSE QMC in J1-J2-J3 model . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.6 Measuring physical quantities in QMC . . . . . . . . . . . . . . . . . . . . . . 27 3 Sign Problems in QMC. . . . . . . . . . . . . . . . . 29 3.1 Sign problem in frustrated J1 − J2 model . . . . . . . . . . . . . . . . . . . . 31 3.2 Sign problem in frustrated J1 − J3 model . . . . . . . . . . . . . . . . . . . . 33 4 Numerical results about the Knight shifts. . . . . . . . . . . . . . . . . . . 36 4.1 Knight shifts in a system with single impurity . . . . . . . . . . . . . . . . . . 38 4.2 Knight shifts in a system with two impurities . . . . . . . . . . . . . . . . . . 39 4.3 Knight shifts on site (1, 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 5 Ground state staggered magnetization. . . . . . . . . . . . . . . . . 45 5.1 Ground state convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 5.2 Reduction of the ground state staggered magnetization . . . . . . . . . . . . . 48 5.3 The slope of the Mst(z) vs. z curve . . . . . . . . . . . . . . . . . . . . . . . . 51 6 Conclusions. . . . . . . .. . . . . . . . . . 54 Bibliography . . . . . .. . . . . .. . 56 | |
| dc.language.iso | en | |
| dc.subject | 隨機序列展開 | zh_TW |
| dc.subject | 高溫超導 | zh_TW |
| dc.subject | 銅氧平面 | zh_TW |
| dc.subject | 反鐵磁磁化率 | zh_TW |
| dc.subject | 量子蒙地卡羅 | zh_TW |
| dc.subject | Quantum Monte Carlo | en |
| dc.subject | Stochastic Series Expansion | en |
| dc.subject | high-Tc cuprate | en |
| dc.subject | Knight shift | en |
| dc.subject | staggered magnetization | en |
| dc.title | 二維量子反鐵磁中的挫折性交互作用 | zh_TW |
| dc.title | Frustrated Interactions in a 2D Quantum Antiferromagnet | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 96-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 管希聖(Hsi-Sheng Goan),郭光宇(Guang-Yu Guo) | |
| dc.subject.keyword | 高溫超導,銅氧平面,隨機序列展開,量子蒙地卡羅,反鐵磁磁化率, | zh_TW |
| dc.subject.keyword | high-Tc cuprate,Stochastic Series Expansion,Quantum Monte Carlo,staggered magnetization,Knight shift, | en |
| dc.relation.page | 57 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2008-07-08 | |
| 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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