臺灣博碩士論文加值系統

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 eect
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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