目錄
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?
7.10 The Wess-Zumino-Witten model
7.11 A (brief) introduction to conformal field theory
7.12 The Wess-Zumino-Witten conformal field theory
7.13 Applications 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
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