• Preface
• Abstract
• Declarations
• Aknowledgements
• 1 Introduction
• Interacting Quantum Many-Body Systems
• Mott Insulators
• Quantum Spin Liquids
• 2 Background
• The Falicov Kimball Model
• The Kitaev Honeycomb Model
• Disorder and Localisation
• 3 The Long Range Falicov-Kimball Model
• The Model
• Methods
• Results
• Discussion and Conclusion
• 4 The Amorphous Kitaev Model
• The Model
• Methods
• Results
• Discussion and Conclusion
• 5 Conclusion
• Appendices
• Evaluation of the Fermion Free Energy
• Particle-Hole Symmetry
• Markov Chain Monte Carlo
• A skeleton implementation of MCMC
• An implementation of the standard MH algorithm
• Our two step MH implementation for models with classical and quantum energy terms
• Lattice Generation
• Lattice Colouring
• The Projector