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系統識別號 U0002-2707200514403300
中文論文名稱 排斥性哈伯模型之廣義自洽場研究及其微擾修正
英文論文名稱 GSCF Study of Repulsive Hubbard Model And Its Perturbation Corrections
校院名稱 淡江大學
系所名稱(中) 物理學系碩士班
系所名稱(英) Department of Physics
學年度 93
學期 2
出版年 94
研究生中文姓名 陳凌硯
研究生英文姓名 Ling-Yan Chen
學號 691180060
學位類別 碩士
語文別 中文
口試日期 2005-06-23
論文頁數 120頁
口試委員 指導教授-楊棨
委員-薛宏中
委員-蔣幼齡
中文關鍵字 哈巴特模型  廣義自洽場  微擾理論 
英文關鍵字 Hubbard Model  generalized self-consistent field  perturbation theory  Bethe-ansatz 
學科別分類 學科別自然科學物理
中文摘要 在本論文中發展一種新的微擾方法對Hubbard 模型之廣義自洽場(GSCF)近似結果做修正. 此微擾方法以 GSCF 解作為零階近似, 比以無交互作用電子系統作為零階近似的傳統微擾方法能在更大的參數範圍中得到收斂結果, 而傳統微擾方法只適用於弱交互作用強度(|U|/t<<1)的情況.
本論文詳細分析一維及二維排斥性Hubbard 模型. 計算基態性質, 包括:能量, 雙重佔據數, 跳躍動能, 並在一維情況下與 Bethe-ansatz 精確解結果做比較. 研究在廣泛電子濃度值,廣泛交互作用強度值,廣泛磁場值下進行. 在一定的 n, U, h 參數範圍中新的微擾近似結果更符合精確解, 且於弱耦合及強耦合極限下與精確解完全符合.
本論文首次做了二維的GSCF 近似計算, 除了以上所提之基態物理量外,還探討了化學勢, 橫向自旋, 縱向自旋, 橫向自旋波矢等量. 在特定的情況下二維系統會呈現順磁態或發生一階相變. 此現象在一維情形中不存在.
英文摘要 In this thesis a new perturbation method is developed to calculate corrections to generalized self-consistent field (GSCF) approximation of the Hubbard model solution. This perturbation method regards the GSCF solution as the zero order approximation and is able to get converging results in a more wide parameter range than the tranditional perturbation method. The tranditional perturbation method regards the system of the non-interacting electrons as the zero order approximation and is suitable only for the weak interaction intensities (|U|/t<<1).
In this thesis the one- and two-dimentional repulsive Hubbard model is analysed in detail . The calculated gound state properties, namely, the energy, the double occupancy andthe kinetic energy are compared with Bethe-ansatz exact results in the one-dimensional case. Investigation is carried out for the general electronic density value, general interaction intensity value, and general magnetic field value. In certain n, U, h ranges, the perturbation and exact results are quite close and they coincide at weak and strong coupling limits.
This thesis for the first time presents the two-dimentional GSCF results. In
addition of the above mentioned ground state physical quantities, the chemical
potential, transverse and longitudinal spin, and the wave verctor of transverse spin are
discussed as well. In the two-dimentional system a paramagnetic state and some one
order phase transitions appear in specific cases. This phenomenon does not exist in the
one-dimensional case.
論文目次 1 前言…..1
2 Hubbard 模型及廣義自洽場(GSCF)近似…..3
2.1 Hubbard 模型…..3
2.2 GSCF 近似…..6
2.3 正則變換…..9
2.4 自洽方程…..12
2.5 自旋結構…..13
2.6 極限情形…..17
2.6.1 一維弱耦合極限…..17
2.6.2 一維強耦合極限…..19
3 Hubbard 模型之微擾理論…..23
3.1 一般微擾理論…..23
3.2 微擾理論 A …..25
3.2.1 一般情形…..25
3.2.2 一維情形…..29
3.3 微擾理論 B …..32
3.3.1 基態波函數近似…..32
3.3.2 一階能量的修正…..34
3.3.3 二階能量的修正…..37
4 數值計算…..43
4.1 GSCF 能量之數值計算…..43
4.2 微擾理論 B 之數值計算…..47
5 一維情形的數值結果…..49
5.1 基態能量…..49
5.2 雙重佔據數…..58
5.3 跳躍動能…..65
5.4 對 q 的變分…..70
6 二維情形的數值結果…..73
6.1 基態能量…..73
6.2 雙重佔據數…..85
6.3 跳躍動能…..90
6.4 化學勢…..95
6.5 自旋…..100
6.6 橫向自旋波矢…..104
7 結論…..109
A Wick 定理…..111
B 無磁場下微擾理論 A 之二階能量…..113
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