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
