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《凝聚态物理学场论》用量子场论的概念阐述了凝聚态中*具挑战的物理学问题，内容论及重正化群、Luttinger液体、规范理论、拓扑流体、拓扑绝缘体和量子纠缠。本书从基本概念入手，依次将读者带入当今物理领域的研究前沿，如物质的拓扑相，量子与经典临界现象，量子霍尔效应和超导。同时，书中还包括一维强相关系统，量子有序相和无序相，以及凝聚态、场论和分形统计学中的拓扑结构。本书主要面向凝聚态、高能物理和弦理论领域，以及数学领域的科技工作者。

Preface to the second edition

Preface to the first edition

1 Introduction

1.1 Field theory and condensed matter physics

1.2 What has been included in this book (first edition)

1.3 What was left out of the first edition

1.4 What has been included in the second edition

2 The Hubbard model

2.1 Introduction

2.2 Symmetries of the Hubbard model

2.3 The strong-coupling limit

2.4 The weak-coupling limit

2.5 Correlation functions

3 The magnetic instability of the Fermi system

3.1 Mean-field theory

3.2 Path-integral representation of the Hubbard model

3.3 Path integrals and mean-field theory

3.4 Fluctuations: the non-linear sigma model

3.5 The Neel state and the non-linear sigma model

4 The renormalization group and scaling

4.1 Scale invariance

4.2 Examples of fixed points

4.3 Scaling behavior of physical observables

4.4 General consequences of scale invariance

4.5 Perturbative renormalization group about a fixed point

4.6 The Kosterlitz renormalization group

5 One-dimensional quantum antiferromagnets

5.1 The spin- 1/2 Heisenberg chain

5.2 Fermions and the Heisenberg model

5.3 The quantum Ising chain

5.4 Duality

5.5 The quantum Ising chain as a free-Majorana-fermion system

5.6 Abelian bosonization

5.7 Phase diagrams and scaling behavior

6 The Luttinger liquid

6.1 One-dimensional Fermi systems

6.2 Dirac fermions and the Luttinger model

6.3 Order parameters of the one-dimensional electron gas

6.4 The Luttinger model: bosonization

6.5 Spin and the Luttinger model

6.6 Scaling and renormalization in the Luttinger model

6.7 Correlation functions of the Luttinger model

6.8 Susceptibilities of the Luttinger model

7 Sigma models and topological terms

7.1 Generalized spin chains: the Haldane conjecture

7.2 Path integrals for spin systems: the single-spin problem

7.3 The path integral for many-spin systems

7.4 Quantum ferromagnets

7.5 The effective action for one-dimensional quantum antiferromagnets

7.6 The role of topology

7.7 Quantum fluctuations and the renormalization group

7.8 Asymptotic freedom and Haldane's conjecture

7.9 Hopf term or no Hopf term?

7.10The Wess-Zumino-Witten model

7.11A (brief) introduction to conformal field theory

7.12The Wess-Zumino-Witten conformal field theory

7.13Applications of non-abelian bosonization

8 Spin-liquid states

8.1 Frustration and disordered spin states

8.2 Valence bonds and disordered spin states

8.3 Spinons, holons, and valence-bond states

8.4 The gauge-field picture of the disordered spin states

8.5 Flux phases, valence-bond crystals, and spin liquids

8.6 Is the large-N mean-field theory reliable?

8.7 SU(2) gauge invariance and Heisenberg models Gauge theory, dimer models, and topological phases

9.1 Fluctuations of valence bonds: quantum-dimer models

9.2 Bipartite lattices: valence-bond order and quantum criticality

9.3 Non-bipartite lattices: topological phases

9.4 Generalized quantum-dimer models

9.5 Quantum dimers and gauge theories

9.6 The Ising gauge theory

9.7 The Z2 confining phase

9.8 The Ising deconfining phase: the Z2 topological fluid

9.9 Boundary conditions and topology

9.10 Generalized Z2 gauge theory: matter fields

9.11 Compact quantum electrodynamics

9.12 Deconfinement and topological phases in the U(1) gauge theory

9.13 Duality transformation and dimer models

9.14 Quantum-dimer models and monopole gases

9.15 The quantum Lifshitz model

10 Chiral spin states and anyons

10.1 Chiral spin liquids

10.2 Mean-field theory of chiral spin liquids

10.3 Fluctuations and flux phases

10.4 Chiral spin liquids and Chern-Simons gauge theory

10.5 The statistics of spinons

10.6 Fractional statistics

10.7 Chern-Simons gauge theory: a field theory of anyons

10.8 Periodicity and families of Chern-Simons theories

10.9 Quantization of the global degrees of freedom

10.10 Flux phases and the fractional quantum Hall effect

10.11 Anyons at finite density

10.12 The Jordan-Wigner transformation in two dimensions

11 Anyon superconductivity

11.1 Anyon superconductivity

11.2 The functional-integral formulation of the Chern-Simons theory

11.3 Correlation functions

11.4 The semi-classical approximation

11.5 Effective action and topological invariance

12 Topology and the quantum Hall effect

12.1 Quantum mechanics of charged particles in magnetic fields

12.2 The Hofstadter wave functions

12.3 The quantum Hall effect

12.4 The quantum Hall effect and disorder

12.5 Linear-response theory and correlation functions

12.6 The Hall conductance and topological invariance

12.7 Quantized Hall conductance of a non-interacting system

12.8 Quantized Hall conductance of Hofstadter bands

13 The fractional quantum Hall effect

13.1 The Laughlin wave function

13.2 Composite particles

13.3 Landau-Ginzburg theory of the fractional quantum Hall effect

13.4 Fermion field theory of the fractional quantum Hall effect

13.5 The semi-classical excitation spectrum

13.6 The electromagnetic response and collective modes

13.7 The Hall conductance and Chern-Simons theory

13.8 Quantum numbers of the quasiparticles: fractional charge

13.9 Quantum numbers of the quasiparticles: fractional statistics

14 Topological fluids

14.1 Quantum Hall fluids on a toms

14.2 Hydrodynamic theory

14.3 Hierarchical states

14.4 Multi-component abelian fluids

14.5 Superconductors as topological fluids

14.6 Non-abelian quantum Hall states

14.7 The spin-singlet Halperin states

14.8 Moore-Read states and their generalizations

14.9 Topological superconductors

14.10 Braiding and fusion

15 Physics at the edge

15.1 Edge states of integer quantum Hall fluids

15.2 Hydrodynamic theory of the edge states

15.3 Edges of general abelian quantum Hall states

15.4 The bulk——edge correspondence

15.5 Effective-field theory of non-abelian states

15.6 Tunneling conductance at point contacts

15.7 Noise and fractional charge

15.8 Quantum interferometers

15.9 Topological quantum computation

16 Topological insulators

16.1 Topological insulators and topological band structures

16.2 The integer quantum Hall effect as a topological insulator

16.3 The quantum anomalous Hall effect

16.4 The quantum spin Hall effect

16.5 Z2 topological invariants

16.6 Three-dimensional topological insulators

16.7 Solitons in polyacetylene

16.8 Edge states in the quantum anomalous Hall effect

16.9 Edge states and the quantum spin Hall effect

16.10 Z2 topological insulators and the parity anomaly

16.11 Topological insulators and interactions

16.12 Topological Mott insulators and nematic phases

16.13 Topological insulators and topological phases

17 Quantum entanglement

17.1 Classical and quantum criticality

17.2 Quantum entanglement

17.3 Entanglement in quantum field theory

17.4 The area law

17.5 Entanglement entropy in conformal field theory

17.6 Entanglement entropy in the quantum Lifshitz universality class

17.7 Entanglement entropy in φ4 theory

17.8 Entanglement entropy and holography

17.9 Quantum entanglement and topological phases

17.10 Outlook

References

Index

Eduardo Fradkin，凝聚态物理、强关联系统、量子霍尔效应和量子场论等领域的知名学者，伊利诺伊大学厄巴纳-香槟分校(University of Illinois at Urbana-Champaign)物理系教授。

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书籍介绍

《凝聚态物理学场论》用量子场论的概念阐述了凝聚态中*具挑战的物理学问题，内容论及重正化群、Luttinger液体、规范理论、拓扑流体、拓扑绝缘体和量子纠缠。本书从基本概念入手，依次将读者带入当今物理领域的研究前沿，如物质的拓扑相，量子与经典临界现象，量子霍尔效应和超导。同时，书中还包括一维强相关系统，量子有序相和无序相，以及凝聚态、场论和分形统计学中的拓扑结构。本书主要面向凝聚态、高能物理和弦理论领域，以及数学领域的科技工作者。