Quantum Scaling in Many Body Systems An Approach to Quantum Phase Transitions 2nd Edition by Mucio Continentino ISBN 1108183735 9781108183734

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ISBN 10:  1108183735
ISBN 13: 978-1108183734
Author:      Mucio Continentino

Quantum Scaling in Many Body Systems An Approach to Quantum Phase Transitions 2nd Table of contents:

1. Scaling Theory of Quantum Critical Phenomena

1.1 Quantum Phase Transitions
1.2 Renormalisation Group and Scaling Relations
1.3 The Critical Exponents
1.4 Scaling Properties Close to a Zero-Temperature Fixed Point
1.5 Extension to Finite Temperatures
1.6 Temperature-Dependent Behaviour near a Quantum Critical Point
1.7 Generalised Scaling
1.8 Conclusions

2. Landau and Gaussian Theories

2.1 Introduction
2.2 Landau Theory of Phase Transitions
2.3 Gaussian Approximation (T > Tₐ)
2.4 Gaussian Approximation (T < Tₐ)
2.5 Goldstone Mode
2.6 Ising Model in a Transverse Field – Mean-Field Approximation

3. Real Space Renormalisation Group Approach

3.1 Introduction
3.2 The Ising Model in a Transverse Field
3.3 Recursion Relations and Fixed Points
3.4 Conclusions

4. Renormalisation Group: the ϵ-Expansion

4.1 The Landau–Wilson Functional
4.2 The Renormalisation Group in Momentum Space
4.3 Fixed Points
4.4 Renormalisation Group Flows and Critical Exponents
4.5 Conclusions

5. Quantum Phase Transitions

5.1 Effective Action for a Nearly Ferromagnetic Metal
5.2 The Quantum Paramagnetic-to-Ferromagnetic Transition
5.3 Extension to Finite Temperatures
5.4 Effective Action Close to a Spin-Density Wave Instability
5.5 Gaussian Effective Actions and Magnetic Instabilities in Metallic Systems
5.6 Field-Dependent Free Energy
5.7 Gaussian versus Mean Field at T ≠ 0
5.8 Critique of Hertz Approach

6. Heavy Fermions

6.1 Introduction
6.2 Scaling Analysis
6.3 Conclusions

7. A Microscopic Model for Heavy Fermions

7.1 The Model
7.2 Local Quantum Criticality
7.3 Critical Regime
7.4 Generalised Scaling and the Non-Fermi Liquid Regime
7.5 Local Regime near the QCP
7.6 Quantum Lifshitz Point
7.7 Conclusions

8. Metal and Superfluid–Insulator Transitions

8.1 Conductivity and Charge Stiffness
8.2 Scaling Properties Close to a Metal–Insulator Transition
8.3 Different Types of Metal–Insulator Transitions
8.4 Disorder-Driven Superfluid–Insulator Transition

9. Density-Driven Metal–Insulator Transitions

9.1 The Simplest Density-Driven Transition
9.2 Renormalisation Group Approach
9.3 Metal–Insulator Transition in Divalent Metals
9.4 The Excitonic Transition
9.5 The Effect of Electron–Electron Interactions
9.6 The Density-Driven MI Transition in the d = 1 Hubbard Model
9.7 Effects of Disorder

10. Mott Transitions

10.1 Introduction
10.2 Gutzwiller Approach
10.3 Density-Driven Transition
10.4 Scaling Analysis
10.5 Conclusions

11. The Non-Linear Sigma Model

11.1 Introduction
11.2 Transverse Fluctuations
11.3 The Quantum Non-Linear Sigma Model
11.4 Some Notable β-Functions

12. Superconductor Quantum Critical Points

12.1 Introduction
12.2 Non-Uniform Superconductor
12.3 Criterion for Superconductivity
12.4 Normal-to-FFLO Quantum Phase Transition in Three Dimensions
12.5 The Universality Class of the T=0 d=3 FFLO Quantum Phase Transition
12.6 The Two-Dimensional Problem
12.7 Disorder-Induced SQCP

13. Topological Quantum Phase Transitions

13.1 The Landau Paradigm
13.2 Topological Quantum Phase Transitions
13.3 The Kitaev Model
13.4 Renormalisation Group Approach to the Kitaev Model
13.5 The Simplest Topological Insulator: the sp-Chain
13.6 Weyl Fermions in Superconductors

14. Fluctuation-Induced Quantum Phase Transitions

14.1 Introduction
14.2 Goldstone Modes and Anderson–Higgs Mechanism
14.3 The Effective Potential
14.4 At the Quantum Critical Point
14.5 The Nature of the Transition
14.6 The Neutral Superfluid
14.7 The Charged Superfluid
14.8 Quantum First-Order Transitions in Systems with Competing Order Parameters
14.9 Superconducting Transition
14.10 Antiferromagnetic Transition
14.11 One-Loop Effective Potentials and Renormalisation Group
14.12 Conclusions

15. Scaling Theory of First-Order Quantum Phase Transitions

15.1 Scaling Theory of First-Order Quantum Phase Transitions
15.2 The Charged Superfluid and the Coleman–Weinberg Potential: Scaling Approach
15.3 Conclusions

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