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Quantum criticality and fidelity in many-body systems. / 多體系統中的量子臨界現象與保真度 / Quantum criticality and fidelity in many-body systems. / Duo ti xi tong zhong de liang zi lin jie xian xiang yu bao zhen du

Kwok, Ho Man = 多體系統中的量子臨界現象與保真度 / 郭灝民. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 106-109). / Abstracts in English and Chinese. / Kwok, Ho Man = Duo ti xi tong zhong de liang zi lin jie xian xiang yu bao zhen du / Guo Haomin. / Chapter 1 --- Overview of Quantum Phase transitions --- p.1 / Chapter 1.1 --- Classification of QPTs --- p.2 / Chapter 1.2 --- Teaching model: The quantum Ising model --- p.4 / Chapter 1.3 --- Critical exponents and universality classes --- p.6 / Chapter 1.4 --- A new tool to the QPT: Fidelity --- p.8 / Chapter 1.5 --- Fidelity susceptibility --- p.12 / Chapter 1.6 --- Motivation of this report --- p.16 / Chapter 2 --- Analysis of the One Dimensional Quantum XY model --- p.17 / Chapter 2.1 --- Introduction to the model Hamiltonian --- p.17 / Chapter 2.2 --- Diagonalizing the Hamiltonian --- p.18 / Chapter 2.2.1 --- Jordan-Wigner transformation --- p.18 / Chapter 2.2.2 --- Bogoliubov transformation --- p.22 / Chapter 2.3 --- Ground state properties --- p.24 / Chapter 2.4 --- Calculating the fidelity susceptibility --- p.25 / Chapter 2.5 --- Fidelity susceptibility in Quantum Ising model --- p.31 / Chapter 2.6 --- Numerical comparison --- p.36 / Chapter 3 --- The Lipkin-Meshkov-Glick model --- p.40 / Chapter 3.1 --- Literature Review --- p.40 / Chapter 3.1.1 --- Scaling Behaviour --- p.41 / Chapter 3.1.2 --- Quantum Phase Transition --- p.42 / Chapter 3.1.3 --- Mathematical formalism --- p.44 / Chapter 3.1.4 --- Conserved quantities --- p.46 / Chapter 3.2 --- Energy spectrum for isotropic case --- p.47 / Chapter 3.3 --- Energy spectrum for anisotropic case --- p.49 / Chapter 3.3.1 --- The Holstein-Primakoff mapping --- p.49 / Chapter 3.3.2 --- Bogoliubov transformation for Boson systems --- p.53 / Chapter 3.4 --- Fidelity susceptibility in the isotropic case --- p.55 / Chapter 3.4.1 --- h> h0 --- p.56 / Chapter 3.4.2 --- h0 > h> h1 --- p.57 / Chapter 3.4.3 --- h1 > h > h2 --- p.57 / Chapter 3.5 --- Fidelity susceptibility in the anisotropic case --- p.60 / Chapter 3.5.1 --- "h > 1, driving by γ - xF(γ)" --- p.60 / Chapter 3.5.2 --- "h > 1, driving by h - xF(h)" --- p.62 / Chapter 3.5.3 --- "h < 1, driving by γ - xF(γ)" --- p.63 / Chapter 3.5.4 --- "h < 1, driving by h - xF(h)" --- p.64 / Chapter 3.6 --- Discussion and numerical analysis --- p.65 / Chapter 3.7 --- A possible resolution to the isotropic case: Partial-state fidelity and its susceptibility --- p.71 / Chapter 3.7.1 --- Review of the formalism --- p.72 / Chapter 3.7.2 --- Continuous level crossing and fidelity in the isotropic model --- p.74 / Chapter 3.7.3 --- Partial-state fidelity susceptibility --- p.77 / Chapter 4 --- Numerical Approach to Fidelity Susceptibility --- p.81 / Chapter 4.1 --- The Scaling Ansatz and Critical exponents --- p.81 / Chapter 4.2 --- Examples --- p.83 / Chapter 4.2.1 --- One Dimensional Quantum Ising model --- p.83 / Chapter 4.2.2 --- LMG model --- p.86 / Chapter 4.2.3 --- Two Dimensional Quantum Ising model --- p.90 / Chapter 4.2.4 --- Two Dimensional XXZ model --- p.93 / Chapter 4.2.5 --- One Dimensional Heisenberg model --- p.96 / Chapter 4.3 --- Discussion --- p.100 / Chapter 5 --- Summary --- p.105 / Bibliography --- p.106

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326480
Date January 2008
ContributorsKwok, Ho Man., Chinese University of Hong Kong Graduate School. Division of Physics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, x, 109 p. : ill. ; 30 cm.
RightsUse 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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