Li, Ying Wai = 安德森模型下量子相變的數值研究 / 李盈慧. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 69-72). / Text in English; abstracts in English and Chinese. / Li, Ying Wai = Andesen mo xing xia liang zi xiang bian de shu zhi yan jiu / Li, Yinghui. / Chapter 1 --- Review on Anderson Models and Quantum Phase Transitions --- p.1 / Chapter 1.1 --- The Anderson Impurity Model --- p.1 / Chapter 1.2 --- The Periodic Anderson Model --- p.2 / Chapter 1.3 --- Quantum Phase Transitions (QPTs) --- p.3 / Chapter 1.4 --- Motivation of this project --- p.4 / Chapter 2 --- Studies on the Ground State Energy of Periodic Anderson Model --- p.7 / Chapter 2.1 --- Background --- p.7 / Chapter 2.2 --- Hamiltonian and Physical Meanings of Lattice Anderson Model --- p.8 / Chapter 2.2.1 --- The first term: -t ´iσ （c+̐ưσci+lσ + h.c.) --- p.8 / Chapter 2.2.2 --- The second term: Ef´iσ̐ưfiσ --- p.9 / Chapter 2.2.3 --- The third term: V ´ ̐ưσ (c+iσ̐ư̐ưσ + h.c.) --- p.9 / Chapter 2.2.4 --- The fourth term: U ̐ưσ´ nfitnfi↓ --- p.9 / Chapter 2.2.5 --- The whole Hamiltonian --- p.10 / Chapter 2.3 --- Non-Interacting Case of Lattice Anderson Model --- p.10 / Chapter 2.3.1 --- The Hamiltonian in momentum space --- p.11 / Chapter 2.3.2 --- The conduction band eK --- p.12 / Chapter 2.3.3 --- The band energies ±K --- p.12 / Chapter 2.3.4 --- The energy band gap Δ --- p.14 / Chapter 2.3.5 --- Green's functions at finite temperature --- p.14 / Chapter 2.4 --- Perturbation in U for symmetric model --- p.16 / Chapter 2.4.1 --- Previous Results --- p.16 / Chapter 2.4.2 --- Ground state energy at finite temperature by time-dependent perturbation theory --- p.18 / Chapter 3 --- Numerical Integration using Wang-Landau Sampling --- p.22 / Chapter 3.1 --- Background --- p.22 / Chapter 3.2 --- Wang-Landau integration --- p.25 / Chapter 3.2.1 --- Description of the method --- p.25 / Chapter 3.2.2 --- Correspondence between Wang-Landau sampling for physical systems and Wang-Landau integration --- p.27 / Chapter 3.3 --- Results --- p.28 / Chapter 3.3.1 --- Application to one- and two-dimensional test integrals . --- p.28 / Chapter 3.3.2 --- An example of a potential application: Perturbative calculation of the lattice Anderson model --- p.31 / Chapter 3.3.3 --- Discussion and summary --- p.35 / Chapter 4 --- Studies on QPT of Anderson Impurity Model by Quantum Entanglement --- p.38 / Chapter 4.1 --- Background --- p.38 / Chapter 4.2 --- Formalism --- p.39 / Chapter 4.2.1 --- Hamiltonian --- p.39 / Chapter 4.2.2 --- Conditions Used in Our Study --- p.40 / Chapter 4.2.3 --- Quantifying Quantum Entanglement: Entropy and Concurrence --- p.41 / Chapter 4.3 --- Numerical Results --- p.45 / Chapter 4.3.1 --- Method --- p.45 / Chapter 4.3.2 --- Finite Size Effects of the Ground State Energy --- p.46 / Chapter 4.3.3 --- Finite Size Effects of the Von Neumann Entropy --- p.49 / Chapter 4.3.4 --- Finite Size Effects of the Fermionic Concurrence --- p.53 / Chapter 4.4 --- Summary --- p.58 / Chapter 5 --- Fidelity in Critical Phenomena --- p.59 / Chapter 5.1 --- Background --- p.59 / Chapter 5.2 --- Ground State Fidelity and Dynamic Structure Factor --- p.60 / Chapter 5.3 --- Mixed-state fidelity and thermal phase transitions --- p.63 / Chapter 5.4 --- Summary --- p.64 / Chapter 6 --- Conclusion --- p.66 / Bibliography --- p.69
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326051 |
| Date | January 2007 |
| Contributors | Li, Ying Wai., 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 | print, xii, 72 leaves : ill. ; 30 cm. |
| 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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