本論文主要包括三種量子蒙地卡羅(QMC)方法的介紹及將其應用到不同的強關聯系統的結果。當中所涉及的強關聯系統主要是兩個不同的量子液體系統--自旋液體及玻色液體。 / 第二章將詳細介紹三個QMC方法，包括針對非零溫巨正則系統的行列式蒙地卡羅方法(DQMC)，針對零溫正則系絶並解決部分負值問題的限制線軌蒙地卡羅方法(CPMC)，及主要應用在非零溫雜質系統上的Hirsch-Fye蒙地卡羅方法(HFQMC)。 / 自發現高溫起導體以後，其奇異特性如具有非費米液體特性的贗能隙(Pseudogap)引起科學界爭論，由此提出很多不同的理論嘗試解釋。RVB是其中一個具代表性的理論，當中把高溫超導體理解成輕度摻雜的莫特絶緣體(Mott insulator)及引入自旋－電荷分離(charge-spin separation)把系統兩個自由度分開處理，具費米特性的自旋子(spinon)及具玻色特性的空穴子(holon)因而產生。這兩種準粒子的特性在解釋高溫超導的奇異性中最為關鍵。 / 第三章將應用DQMC及CPMC研究擁有各向及各自旋相異費米面的吸引勢赫伯德模型。模型的起源在於有理論[1]提出玻色子的基態有可能因阻挫作用而不發生愛因斯坦-玻色凝聚，這種非凝聚的基態稱為d-波玻色液體。在本研究所採用的模型中，將由庫柏電子對取代原先的正則玻色子。模型在準一准雙排梯子晶格的特性最近已被密度矩阵重整化群(DMRG)方法詳細研究[2]，而本研究將率先使用QMC方法研究模型在準一維雙排、四排梯子及二維正方晶格的特性。QMC有部分證據顯示電子對液體確實在二維存在，在本論文中會作出交代。 / 第四章將應用CPMC研究阻挫作用(frustration)下的排斥勢赫伯德模型，而其具體晶格情況為在正方格子上加上單向斜線躍遷項，稱為t-t'-TH模型。有證據提出在此模型中有可能存自旋液體的基態，並可有效解釋最近在實驗中所觀察到的有機超導體超低溫自旋無序的特性[3]。t-t'-TH模型的導帶半滿情況被曾各種方法詳細研究，本項研究將採用不同 的導帶填充情況及阻挫作用強度，用其比較以觀察阻挫作用對模型基態自旋作用的影響。研究發現阻挫作用將對不同的長程自旋序作出不同程度的影響。 / 第五章則會說明HFQMC的可能應用，在雜質系統如安德遜模型中，HFQMC是研究其非零溫特性的有效方法。此外，這章亦會交代未來在這方面可能進行的研究，而最後一章則會總結全文。 / In this thesis, three quantum Monte Carlo(QMC) algorithms would be reviewed, including determinant Quantum Monte Carlo (DQMC), constraint path Quantum Monte Carlo(CPMC) and Hirsch-Fye Quantum Monte Carlo (HFQMC). These QMC methods would be used to study strongly correlated system. In chapter 3 and 4, DQMC and CPMC methods would be used to study two kinds of quantum liquid, Bose liquid and spin liquid. In chapter 5, the possible application of HFQMC would be discussed. / After the discovery of high T{U+ABB1} cuprate, intensive effort has been paid to construct its theoretical explanation. One of the most puzzling features in cuprate is the pseudogap(strange-metal) phase with non-Fermi liquid behaviour. To search for an non-Fermi liquid to represent this phase, resonating valence bond(RVB) theory proposed a picture of lightly doped spin liquid. Fermionic spinon and bosonic holon arise from the spin-charge separation, and the behaviors of these quasi-particle are important for explanation for high T{U+ABB1} superconductivity. / In chapter 3, we study possible Bose liquid. Motrunich and Fisher [1] proposed a possible uncondensed bosonic phase d-wave Bose liquid(DBL) which will not undergo BEC at ground state. A prior studies[2] has shown that Cooper pairs can be used to replace bosons and N-leg ladder lattice could be used to approach behaviour of 2D lattice. Inspired by them, determinant quantum Monte Carlo(DQMC) and constraint path Monte Carlo(CPMC) techniques are used to study the fermionic attractive Hubbard Model with spin-independent anisotropic Fermi surface. The probable (Local) Cooper Pair Bose metal is detected in 2-leg, 4-leg ladder and 2D lattice. / In chapter 4, we study possible spin liquid. The Hubbard model on an anisotropic triangular lattice called t - t¹ - TH model has been proposed to possess a non-magnetic insulating(spin liquid) state, induced by geometrical frustration. The effect of filling and degree of frustration on magnetic property is investigated by CPMC in the studies. / Chapter 5 is devoted to introducing the usages and possible research projects related to HFQMC. HFQMC is a quantum Monte Carlo method based on path integral formalism, and it is an efficient way to study impurity model at low temperature. A physical background of impurity model is also reviewed. In the last chapter, we would summarize this thesis by comparing the QMC methods used and discussing the result obtained. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Tang, Ho Kin = 強關聯系統的量子蒙地卡羅方法研究 / 鄧皓鍵. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 83-88). / Abstracts also in Chinese. / Tang, Ho Kin = Qiang guan lian xi tong de liang zi Mengdi Kaluo fang fa yan jiu / Deng Haojian. / Chapter 1 --- Introduction to Strongly Correlated System: High T{U+ABB1} superconductivity and Quantum Liquid --- p.1 / Chapter 1.1 --- Types of strongly correlated electron systems --- p.1 / Chapter 1.2 --- High T{U+ABB1} superconductivity --- p.3 / Chapter 1.2.1 --- Phase diagram --- p.4 / Chapter 1.2.2 --- Mott insulator and Anti-ferromagnetic(AFM) order --- p.6 / Chapter 1.2.3 --- Spin-glass --- p.7 / Chapter 1.2.4 --- Pseudogap --- p.7 / Chapter 1.2.5 --- Superconducting --- p.7 / Chapter 1.2.6 --- The complexity and related theory --- p.7 / Chapter 1.3 --- Importance of quantum liquids in high T{U+ABB1} superconductivity --- p.10 / Chapter 1.3.1 --- Spin liquid --- p.10 / Chapter 1.3.2 --- Bose Liquid --- p.11 / Chapter 2 --- Methods --- p.12 / Chapter 2.1 --- Introduction to Quantum Monte Carlo --- p.12 / Chapter 2.2 --- Determinant Quantum Monte Carlo(DQMC) --- p.13 / Chapter 2.2.1 --- Purpose of DQMC --- p.13 / Chapter 2.2.2 --- Overall information of DQMC --- p.14 / Chapter 2.2.3 --- Green function in DQMC --- p.20 / Chapter 2.2.4 --- Observable measurement --- p.21 / Chapter 2.2.5 --- Numerical Implementation --- p.24 / Chapter 2.2.6 --- Limitation --- p.26 / Chapter 2.3 --- Constraint Path Quantum Monte Carlo(CPMC) --- p.26 / Chapter 2.3.1 --- Purpose of CPMC --- p.26 / Chapter 2.3.2 --- Algorithm discussion --- p.28 / Chapter 2.3.3 --- Implementation Issues --- p.32 / Chapter 2.4 --- Hirsch-Fye Quantum Monte Carlo(HFQMC) --- p.35 / Chapter 2.4.1 --- Algorithm outline --- p.35 / Chapter 2.4.2 --- Program Structure --- p.38 / Chapter 3 --- A Possible Realization of Bose Liquid: Attractive Hubbard Model with Spin-dependent Anisotropic Hopping --- p.41 / Chapter 3.1 --- Idea of Bose metal --- p.41 / Chapter 3.2 --- Model Hamiltonian --- p.44 / Chapter 3.3 --- Phases and its detection --- p.45 / Chapter 3.3.1 --- Measurement --- p.45 / Chapter 3.3.2 --- Phases --- p.46 / Chapter 3.4 --- Multi-leg ladder Lattice --- p.47 / Chapter 3.4.1 --- Band structure --- p.47 / Chapter 3.4.2 --- Two-leg ladder: Cooper-pair Bose Metal Phase --- p.51 / Chapter 3.4.3 --- Four-leg ladder: Cooper-pair Bose Metal Phase --- p.55 / Chapter 3.5 --- 2D Lattice --- p.56 / Chapter 3.5.1 --- Band structure --- p.56 / Chapter 3.5.2 --- 2D Lattice: Local Cooper-pair Bose Metal(LCPBM) Phase --- p.60 / Chapter 3.6 --- Summary --- p.61 / Chapter 4 --- A Possible Realization of Spin Liquid: Square Lattice Hubbard Model with Geometrical Frustration --- p.65 / Chapter 4.1 --- Frustration and Spin Liquid --- p.65 / Chapter 4.1.1 --- Physical systems --- p.66 / Chapter 4.1.2 --- Recent developments of t-t’-TH model --- p.67 / Chapter 4.2 --- Model Hamiltonian --- p.67 / Chapter 4.3 --- Band structure --- p.68 / Chapter 4.4 --- Frustration Effect on Magnetism --- p.70 / Chapter 4.5 --- Summary --- p.73 / Chapter 5 --- Possible Application of HFQMC --- p.75 / Chapter 5.1 --- Anderson Model --- p.75 / Chapter 5.1.1 --- Physical Issues --- p.75 / Chapter 5.1.2 --- Model proposal and mean field result --- p.76 / Chapter 5.1.3 --- Properties of model with quantum degree of freedom --- p.77 / Chapter 5.2 --- The application cases --- p.78 / Chapter 6 --- Summary --- p.80 / Chapter 6.1 --- Three QMC methods --- p.80 / Chapter 6.2 --- Two practical models --- p.80 / Bibliography --- p.83
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328590 |
| Date | January 2012 |
| Contributors | Tang, Ho Kin., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (xii, 88 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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