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研究生:魯崇磊
研究生(外文):Chung-Lei Lu
論文名稱:一維哈巴特模型廣義自洽場結果及其微擾修正
論文名稱(外文):Generalized Self-consistent Field Results of One-dimensional Hubbard Models And Their Perturbation Corrections
指導教授:楊 棨 
指導教授(外文):Professor Chi Yang
學位類別:碩士
校院名稱:淡江大學
系所名稱:物理學系
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
中文關鍵詞:哈巴特模型弱耦合極限強耦合極限廣義自洽場微擾理論
外文關鍵詞:Hubbard modelgeneralized self-consistent fieldground-state propertiesperturbation theory
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  • 被引用被引用:0
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  • 下載下載:9
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本論文針對 Hubbard 模型在交互作用強度從負無限大到正無限大, 電子濃度, 討論其基態性質, 包括能量, 化學勢, 雙重佔據結點濃度, 動能及序參數, 並且作為 U 的函數分析其行為; 也針對極限情形,包括弱耦合極限及強耦合極限, 加以解析討論。
另外, 雖然廣義自洽場 (GSCF) 近似的結果和精確的結果比較, 在一維情形下有不錯的吻合程度, 但是仍然有一定程度的差別, 本文利用微擾理論,發展兩種方法 (微擾理論 A 及微擾理論 B), 對廣義自洽場 (GSCF) 近似的結果朝向精確的結果做二級修正。
本文主要研究在於一維GSCF近似解與精確解之比較, 加上微擾修正後, 我們給出廣泛的物理圖像, 建立一個堅實的基礎, 使得模型在二維甚至二維以上的研究能有可靠的參考依據。

The ground-state properties of the one-dimensional Hubbard model within the generalized self-consistent field (GSCF) approach are discussed in the entire range of interaction strength. The ground state energy, chemical potential, double occupancy, kinetic energy and order parameter are calculated and analyzed as functions of interaction strength U. The limiting cases of weak and strong coupling are discussed.
The results of GSCF approach fit the exact ones quite well, but there are still some deviations. We develop two versions of perturbation theory (A and B) to improve the approximation.
The main goal of this research is to compare one-dimensional GSCF results with that of the exact solution. After perturbation corrections we obtain a general physical picture and a solid basis for the Hubbard model of two or higher dimensions.

第一章 前言-----------------------------------------1
第二章 Hubbard模型----------------------------------3
第三章 廣義自洽場(GSCF)近似-------------------------5
第四章 GSCF結果與精確結果之比較---------------------29
第五章 微擾理論概述---------------------------------57
第六章 Hubbard模型之微擾理論 A----------------------59
第七章 Hubbard模型之微擾理論 B----------------------65
第八章 結論-----------------------------------------97

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