Quantum Scaling in Many Body Systems An Approach to Quantum Phase Transitions 2nd Edition by Mucio Continentino ISBN 1107150256 978-1107150256

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ISBN 10: 1107150256
ISBN 13: 978-1107150256
Author: Mucio Continentino

Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.

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 > T[sub(c)])

2.4 Gaussian Approximation (T < T[sub(c)])

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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Tags: Mucio Continentino, Quantum Scaling, Phase Transitions