Quantum scaling in many-body systems /
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| Author / Creator: | Continentino, Mucio A. (Mucio Amado) |
|---|---|
| Imprint: | Singapore : World Scientific, c2001. |
| Description: | xiv, 188 p. : ill. ; 23 cm. |
| Language: | English |
| Series: | World Scientific lecture notes in physics vol. 67 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4416075 |
Table of Contents:
- Preface
- Chapter 1. Scaling Theory of Quantum Critical Phenomena
- 1.1. Quantum Phase Transitions
- 1.2. Renormalization Group and Scaling Relations
- 1.3. The Critical Exponents
- 1.4. Scaling Properties Close to a Zero Temperature Fixed Point
- 1.4.1. Irrelevant Variables
- 1.4.2. The Special Role of Time and the Dynamic Exponent
- 1.4.3. The Correlation Function at T = 0
- 1.5. Extension to Finite Temperatures
- 1.5.1. The Crossover Line and the Exponent [phi] = vz
- 1.5.2. The Critical Line and the Shift Exponent [psi]
- 1.5.3. Temperature Dependent Behavior at a Quantum Critical Point
- 1.5.3.1. Naive Scaling
- 1.5.3.2. General Case
- Chapter 2. Landau and Gaussian Theories
- 2.1. Introduction
- 2.2. Landau Theory of Phase Transitions
- 2.2.1. Ising Model in a Transverse Field
- 2.3. Gaussian Approximation (T [ T[subscript c])
- 2.3.1. Ginzburg Criterion
- 2.4. Gaussian Approximation (T [ T[subscript c])
- 2.5. Goldstone Mode
- Chapter 3. Renormalization Group: the [epsiv]-expansion
- 3.1. The Landau-Wilson Functional
- 3.2. The Renormalization Group
- 3.2.1. Slow Modes
- 3.2.2. Integration of Fast Modes
- 3.2.3. Fixed Points
- 3.2.4. Renormalization Group Flows and Critical Exponents
- Chapter 4. Quantum Phase Transitions
- 4.1. Effective Action for a Nearly Ferromagnetic Metal
- 4.2. The Quantum Paramagnetic-to-Ferromagnetic Transition
- 4.2.1. Slow Modes
- 4.2.2. Integration of Fast Modes
- 4.2.3. A Simplified Cut-off
- 4.3. Extension to Finite Temperatures
- 4.4. Effective Action Close to a Spin Density Wave Instability
- 4.5. Gaussian Effective Actions
- 4.6. Field-Dependent Free Energy
- 4.6.1. Gaussian versus Mean-Field at T [not equal] = 0
- Chapter 5. Real Space Renormalization Group Approach
- 5.1. Introduction
- 5.2. The Ising Model in a Transverse Field
- 5.2.1. Recursion Relations and Fixed Points
- 5.3. Conclusion
- Chapter 6. Heavy Fermions
- 6.1. Introduction
- 6.2. Scaling Analysis
- 6.3. Conclusions
- Chapter 7. A Microscopic Model for Heavy Fermions
- 7.1. Introduction
- 7.2. Susceptibility and Wilson Ratio
- 7.3. Resistivity and Kadowaki-Woods Ratio
- 7.4. Critical Regime
- 7.5. Local Regime and One-Parameter Scaling
- 7.6. Generalized Scaling and the Non-Fermi Liquid Regime
- 7.6.1. Local Regime at the QCP
- 7.7. Quantum Lifshitz Point
- 7.8. Conclusions
- Chapter 8. Metal-Insulator Transitions
- 8.1. Conductivity and Charge Stiffness
- 8.2. Scaling Properties Close to a Metal-Insulator Transition
- 8.2.1. Charge Stiffness and Conductivity Mass
- 8.2.2. Thermal Mass
- 8.3. Different Types of Metal-Insulator Transitions
- Chapter 9. Density-Driven Metal-Insulator Transitions
- 9.1. The Simplest Density-Driven Transition
- 9.1.1. Renormalization Group Approach
- 9.2. Metal-Insulator Transition in Divalent Metals
- 9.3. The Excitonic Transition
- 9.4. The Effect of Electron-Electron Interactions
- 9.4.1. The Density-Driven MI Transition in the d = 1 Hubbard Model
- 9.5. Effects of Disorder
- Chapter 10. Mott Transitions
- 10.1. Introduction
- 10.2. Gutzwiller Approach
- 10.2.1. The Kinetic Energy Term
- 10.2.1.1. First Gutzwiller's Hopping
- 10.2.1.2. Second Gutzwiller's Hopping
- 10.2.1.3. Third and Fourth Gutzwiller's Hoppings
- 10.2.2. Relevant Limits
- 10.2.3. Properties of the Solution
- 10.2.4. Ground State Energy
- 10.2.5. Calculation of Thermodynamic Quantities
- 10.2.6. Susceptibility
- 10.2.7. Nearly Half-Filled Band and Arbitrary U
- 10.2.8. Chemical Potential and Compressibility for U [less than or equal] U[subscript c]
- 10.2.9. Chemical Potential for U [greater than or equal] U [subscript c]
- 10.2.10. Density-Driven Transition
- 10.3. Scaling Analysis
- 10.3.1. Correlation Induced or Fixed Density Mott Transition
- 10.3.2. Density-Driven Mott Transition
- 10.3.3. Critical Trajectory
- 10.4. Conclusions
- Chapter 11. The Non-Linear Sigma Model
- 11.1. Introduction
- 11.1.1. Transverse Fluctuations
- 11.2. The Quantum Non-linear Sigma Model
- Chapter 12. Fluctuation-Induced Quantum Phase Transitions
- 12.1. Introduction
- 12.2. Goldstone Modes and Anderson-Higgs Mechanism
- 12.3. The Effective Potential
- 12.4. At the Quantum Critical Point
- 12.5. The Nature of the Transition
- 12.6. The Phase Diagram
- 12.6.1. The Charged Superfluid
- 12.7. Quantum First Order Transitions
- Bibliography
- Index
