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Intro; Supervisor's Foreword; Abstract; Parts of this thesis have been published in the following journal articles:; Acknowledgements; Contents; Abbreviations; 1 Introduction; 1.1 What is ``Physics''?; 1.1.1 A Brief Introduction of Its History; 1.1.2 The Grand Unification; 1.1.3 The Future of Physics; 1.2 High-Tc Copper Oxide Superconductivity; 1.2.1 The Density Waves; 1.2.2 The Pseudo-Gap Phase; 1.3 Correlated Electrons Under Strong Magnetic Field; References; 2 Renormalized Mean Field Theory; 2.1 BdG Equation of Mean-Field Hamiltonian; 2.2 Green's Function and LDOS
4.2 Uniform and Modulated Singlet Flux Phase4.3 Fully Polarized Electron Systems; 4.4 Topological Properties; References; 5 Conclusions and Outlooks; 5.1 Envisions for the High-Tc Problem; 5.2 The Next Era of Magnetism; References; A Exact Diagonalization; A.1 Model; A.2 Many-Body Chern Number; A.3 Results; B Induced Topological-Trivial Transition; References
4.2 Uniform and Modulated Singlet Flux Phase4.3 Fully Polarized Electron Systems; 4.4 Topological Properties; References; 5 Conclusions and Outlooks; 5.1 Envisions for the High-Tc Problem; 5.2 The Next Era of Magnetism; References; A Exact Diagonalization; A.1 Model; A.2 Many-Body Chern Number; A.3 Results; B Induced Topological-Trivial Transition; References