Contents

• List of Tables
• List of Figures
• 1. Introduction
  • 1.1 Strongly Correlated Electron systems
  • 1.2 Models
    • 1.2.1 The Kondo Model
    • 1.2.2 The Hubbard Model
  • 1.3 Methods
  • 1.4 Organization
  • Bibliography
  
  
• 2. Semi-analytical solution of the Kondo model in a magnetic field
  • 2.1 Introduction
  • 2.2 Mapping to a resonant level model
    • 2.2.1 Principles of the flow-equation method
    • 2.2.2 Equivalence to a resonant level model
    • 2.2.3 Calculation of physical quantities
  • 2.3 Results
  • 2.4 Summary and outlook
  • Bibliography
  
  
• 3. Multi-scale Extensions to Quantum Cluster Methods for Strongly Correlated Electron Systems
  • 3.1 Introduction
  • 3.2 Formalism
    • 3.2.1 DCA
    • 3.2.2 Multi Scale Method
    • 3.2.3 A Conserving Approximation
    • 3.2.4 Ansatz
  • 3.3 Approximations to the vertex
    • 3.3.1 First Order in
    • 3.3.2 Second Order in
    • 3.3.3 Full QMC vertex
  • 3.4 Technical Aspects
  • 3.5 Results
    • 3.5.1 First Order in
    • 3.5.2 Second order in
    • 3.5.3 Full QMC Vertex
    • 3.5.4 Real Space Ansatz
  • 3.6 Numerical Considerations and Outlook
  • 3.7 Conclusion
  • Bibliography
  
  
• 4. Spectral Properties of Holstein and Breathing Polarons
  • 4.1 Introduction
  • 4.2 Formalism
    • 4.2.1 Model
    • 4.2.2 Electron-Phonon Coupling
    • 4.2.3 Method
  • 4.3 Results
  • 4.4 Discussion
  • 4.5 Conclusions
  • 4.6 APPENDIX - Effective coupling
    • 4.6.1 Holstein
    • 4.6.2 Breathing
  • Bibliography