文摘
英文文摘
Preface
Chapter 1 Introduction
1.1 Kondo Problem
1.2 Models
1.3 Development history of the NRG
1.4 Outline of the thesis
Chapter 2 Technical details of Wilson's NRG
2.1 The main algorithm
2.1.1 logarithmic discretization
2.1.2 mapping onto the semi-infinite chain hamiltonian
2.1.3 iterative diagonalization
2.2 The graphic representation of the states
2.3 Issues about the symmetry
2.3.1 Spin SU(2) symmetry
2.3.2 pseudo-Spin SU(2) symmetry
2.4 Fixed point analysis
Chapter 3 Recent developments and applications of the NRG
3.1 Calculation of the dynamic quantities
3.2 Improvement on the calculation of spectral function
3.3 Oliveira's z trick
3.4 Bulla's bosonic NRG
3.5 Hofstetter's Density-Matrix NRG
Chapter 4 NRG+DMFT
4.1 DMFT
4.2 An informal derivation of the DMFT algorithm
4.3 NRG+DMFT
Chapter 5 Time-Dependent NRG
5.1 Algorithm
5.1.1 Preliminaries
5.1.2 Algorithm
5.1.3 Benchmark
5.2 Bose-Fermi Kondo model
5.2.1 Model
5.2.2 Motivations
5.2.3 NRG implementation
5.3 Project and Results
Chapter 6 Inclusion
Appendix A NRG implementation for the RLM
Appendix B NRG formula for different symmetries
B.1 U(1)(◎)U(1) symmetry
B.2 SU(2)(◎)U(1) symmetry
B.3 U(1)(◎)SU(2) symmetry
B.4 SU(2)(◎)SU(2) symmetry
Appendix C Comments on the TD-NRG
C.1 Completeness of the basis set
C.2 Derivation of the TD-NRG formula
C.3 z-average
Appendix D Error analysis
Bibliography
