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研究生： 施宏燕
Shih, Hong-Yan
論文名稱： Scaling Ansatz in Renormalization Group Transformations
指導教授： 林秀豪
Lin, Hsiu-Hau
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2010
畢業學年度： 98
語文別： 英文
論文頁數： 64
中文關鍵詞： 重整化群 、準一維 、強關聯 、相變 、相關耦合 、尺度 、超導 、鐵基 、高溫超導 、聲子
外文關鍵詞： renormalization group, quasi-one dimensional, strong correlated, phase transition, relevant coupling, scaling, superconductivity, iron based, high temperature superconductor, phonon
相關次數： 點閱：2  下載：0 
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    • The phase diagram for the interacting fermions in weak coupling is described by the perturbative renormalization group (RG) equations. However, these non-linear differential equations are not analytical, and the relevancy of couplings is difficult to tell in the numerical results. The scaling Ansatz we propose here is a breakthrough not only to predict the scale of the energy gap but also to classify the relevant couplings by building up a hierarchy of them. Applying the scheme to the two-leg ladder, we solve the long-standing phase problem and show that the mismatch of velocity leads no quantum phase transition. Further we investigate the influence of electron-phonon interactions in the fermionic ladders and find that the scaling Ansatz predicts a new type of superconductivity, Coulomb superconductors, emerging from repulsive interactions in the electron pair. In iron-pnictides superconductors, the inter-electron couplings are dominant and drive the electron-phonon couplings to become relevant, which is called the dressed Coulomb type. The scaling Ansatz also explains the anomalous isotope effect in experiments and predicts an extended s-wave pairing in spin gaps.

    1 Introduction 2 The Scaling Ansatz 3 RG Analysis and Phase Transition in Quasi-one Dimension 3.1 Ladder system Hamiltonian 3.2 Renormalization group recipe and one-loop analysis 3.3 Bosonization strategy 3.4 Scaling analysis and quantum phase transition in the two-leg ladder 4 Coulomb Superconductivity in Iron-pnictides 4.1 Ladder model for iron-pnictides 4.2 Electron-phonon interaction in full RG scheme analysis 4.3 Dressed Coulomb phase and anomalous isotope e ect 4.4 Operator tendency method for superconductivity ordering 5 SU(4) Ladder Model for Iron-pnictides Superconductors 5.1 Four-chain model with SU(2)*(Z2*Z2)^2 and SU(4) symmetry 5.2 Bosonization strategy 5.3 Klein factors 5.4 Discussion 6 Conclusion and Outlook Appendix SU(N) RG equations dictionary

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