Mott hubbard Metal insulator Transition and Optical Conductivity in High Dimensions 1st Edition by Nils Blumer ISBN 3832223207 9783832223205 by Nils Blumer 3832223207 instant download after payment.

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ISBN 10: 3832223207 
ISBN 13: 9783832223205
Author: Nils Blumer

Mott hubbard Metal insulator Transition and Optical Conductivity in High Dimensions 1st Table of contents:

Chapter 1: Introduction to Metal-Insulator Transitions and Strong Electron Correlations

• 1.1 Conductors, Insulators, and Semiconductors: A Brief Review of Band Theory
• 1.2 The Mott Insulator: Beyond Band Theory (Mott's Original Idea)
• 1.3 The Hubbard Model: A Minimal Model for Strong Correlations
• 1.4 The Challenge of Many-Body Physics in Condensed Matter
• 1.5 Overview of the Metal-Insulator Transition (MIT) Landscape
• 1.6 Scope and Organization of This Work

Chapter 2: Theoretical Framework: Dynamical Mean-Field Theory (DMFT)

• 2.1 Introduction to Mean-Field Theories in Physics
• 2.2 The Limit of Infinite Dimensions (d=∞): Simplification and Exactness
• 2.3 Mapping the Lattice Problem to an Impurity Problem (Anderson Impurity Model)
• 2.4 The Self-Consistency Condition in DMFT
• 2.5 Numerical Methods for Solving the Impurity Problem (e.g., Iterated Perturbation Theory (IPT), Numerical Renormalization Group (NRG), Quantum Monte Carlo (QMC), Exact Diagonalization (ED))
• 2.6 Advantages and Limitations of DMFT

Chapter 3: The Single-Band Hubbard Model in High Dimensions

• 3.1 Definition of the Single-Band Hubbard Hamiltonian
• 3.2 Phase Diagram of the Hubbard Model in d=∞ (Temperature-Interaction Plane)
• 3.3 The Mott Transition at Half-Filling: First-Order vs. Second-Order
• 3.4 Spectral Properties: Density of States (DOS) in the Metallic and Insulating Phases
• 3.5 Green's Functions and Self-Energies

Chapter 4: Optical Conductivity: Theory and Computation

• 4.1 Definition of Optical Conductivity σ(ω) and its Relation to Current-Current Correlation Functions
• 4.2 Kubo Formula and Linear Response Theory
• 4.3 Optical Conductivity in DMFT: General Formalism
• 4.4 Contributions to Optical Conductivity (Interband vs. Intraband)
• 4.5 Analytical and Numerical Approaches for σ(ω) in the Hubbard Model

Chapter 5: Results on the Mott-Hubbard Transition and Optical Conductivity

• 5.1 Numerical Solutions of DMFT Equations for Various Parameters
• 5.2 Temperature Dependence of the Optical Conductivity across the MIT
• 5.3 Frequency Dependence of σ(ω): Drude Peak, Mid-Infrared Peak, Interband Transitions
• 5.4 Effects of Doping on the Mott Transition and Optical Response
• 5.5 Comparison with Experimental Data (e.g., V$_2$O$_3$, other transition metal oxides)
• 5.6 Discussion of Anomalous Spectral Weight Transfer and its Physical Origin

Chapter 6: Extensions and Further Considerations (Optional, depending on specific content)

• 6.1 Multi-Orbital Hubbard Models and Orbital-Selective Mott Transitions
• 6.2 Effects of Frustration or Disorder in High Dimensions
• 6.3 Finite-Dimensional Corrections to DMFT
• 6.4 Non-Equilibrium Phenomena and Pump-Probe Spectroscopy

Chapter 7: Summary and Outlook

• 7.1 Key Findings of the Research
• 7.2 Implications for Understanding Strongly Correlated Materials
• 7.3 Limitations of the Current Work
• 7.4 Future Research Directions and Open Questions

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Tags: Nils Blumer, hubbard, Metal