臺灣博碩士論文加值系統

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

\bibitem{pet} Peter Brusov, {\it "Mechanisms of high temperature superconductivity"}, Rostov on Don :Rostov State University Publishing,1999.
\bibitem{hpm}{\it "The Hubbard Model Its Physics and Mathematical Physics"}, edited by Dionys Baeriswyl and David K. Campbell etc, 1995, ISBN 0-306-45003-8.
\bibitem{the} {\it "The Hubbard Model"}, edited by Arianna Montorsi, 1992, ISBN 981-02-0585-6.
\bibitem{huu} {\it "Hubbard Model and Anyon Superconductivity"}, edited by A.P. Balachandran and E. Ercolessi etc, 1990, ISBN 981-02-0349-7.
\bibitem{bet} E. H. Lieb and F. Y. Wu., {\it "Absence of mott transition in an exact solution of the short-range, one-band model in one dimension"}, Phys. Rev. Lett. 20, 1445 (1968)
\bibitem{cyy} A. N. Kocharian, C. Yang, Y. L. Chiang, {\it "Self-consistent and exact studies of pairing correlations and crossover in the one-dimensional attractive Hubbard model"}, Phys. Rev. B 59, 7458 (1999).
\bibitem{ylc} Y.-L. Chiang, {\it "Main properties of the one-dimensional Hubbard model in an external magnetic filed"}, Ph. D dissertation, Department of Physics Tamkang University, Tamsui, Taiwan, R. O. C. (2000).
\bibitem{tyc} T.-Y. Chou, {\it "GSCF study of the Magnetic Ground State Properties of One-dimensional Repulsive Hubbard Model"},Master dissertation, Department of Physics Tamkang University, Tamsui, Taiwan, R. O. C.(2001).
\bibitem{mt1} M. Takahashi, {\it "Magnetic susceptibility for the half-filled Hubbard model"}, Progr. Theor. Phys. 42, 1098 (1969); ibid, {\it "Ground state energy of the one-dimensional electron system with short-range interaction."}, I44, 348 (1970); ibid, {\it "Magnetic susceptibility for the half-filled Hubbard model"}, 43, 1619(1970).
\bibitem{kj2} K.-J.-B. Lee and P. Schlottmann, {\it "Thermodynamic Bethe-ansatz equations for the Hubbard chain with an attractive interaction"}, Phys. Rev. B 38, 11566 (1988); ibid, {\it "Low-temperature properties of the Hubbard chain with an attractive interaction"} ,B 40, 9104(1989).
\bibitem{hf3} H. Frahm, and V. E. {\it "Critical exponents for the one-dimensional Hubbard model"}, Jorepin, Phys. Rev. B 42, 10553 (1990).
\bibitem{nk4} N. Kawakami, A. Okiji, {\it "Progress of Theor Physics"}. Supplement No. 101, 429 (1990).
\bibitem{vy5} V. Ya. Krivnov and A. A. Ovchinnikov, {\it "One-dimensional Fermi gas with attraction between the electronsSov"}. Phys. JETP 40, 781 (1975).
\bibitem{tb6} T. B. Bahder and F. Woynarovich, {\it "Gap in the spin excitations and magnetization curve of the one-dimensional attractive Hubbard model"}, Phys. Rev. B 33,2114 (1986).
\bibitem{pth} {\it "Quantum Mechanics"}, by Lesle E. Ballentine, ISBN 0-13-746843-1.
\bibitem{whp} Willam H. Press, Saul A. Teukolsky, Willam T. Vetterling, Brian P. Flannery, {\it "Numerical Recipes in fortran"}, Second Edition, Cambridge University Press.
\bibitem{cay} C. Yang, A. N. Kocharian, Y. L. Chiang, {\it "Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field"}, J. Phys: Condens. Matter 12, 7433-7454 (2000).
\bibitem{fme} F. Marsiglio, Evaluation of the BCS approximation for the attractive Hubbard model in one dimension, Phys. Rev. B 55, 575 (1997).
\bibitem{cya} C. Yang, A. N. Kocharian, Y. L. Chiang, Exact ground-state properties of one-dimensional Hubbard model in the presence of magnetic field, Inter. J. Mod. Phys. B 29-31, 3573(1999).
\bibitem{mathh}{\it "Handbook of Mathematical Functions"}, edited by M. Abramowitz and L.E. Stegun