Chapter
2.5 Fluctuations at the second-order phase transitions
2.5.1 Critical indices and scaling relations
2.6 Quantum phase transitions
2.7 General considerations
2.7.1 Different types of order parameters
2.7.3 Broken symmetry and driving force of phase transitions
2.7.4 The Goldstone theorem
3 Bose and Fermi statistics
4.3 Physical properties of crystals in the harmonic approximation
4.4.3 Another approach to melting. Quantum melting
4.4.4 Low-dimensional solids; why is our world three-dimensional?
5.2 Weakly interacting Bose gas
5.3 Bose condensation and superfluidity
5.3.1 Landau criterion of superfluidity
5.3.2 Vortices in a superfluid
6.1 Basic notions; different types of magnetic response
6.1.1 Susceptibility of noninteracting spins
6.2 Interacting localized moments; magnetic ordering
6.2.1 Mean field approximation
6.2.2 Landau theory for ferromagnets
6.2.3 Antiferromagnetic interactions
6.3 Quantum effects: magnons, or spin waves
6.3.1 Magnons in ferromagnets
Another way to treat spin waves
6.3.2 Antiferromagnetic magnons. Zero-point oscillations and their role
6.4.1 One-dimensional models
(1a) 1d Ising model with nearest-neighbour interaction
(1b) 1d xy model, spins 1/2
(1c) 1d Heisenberg model for S = 1/2
6.4.2 Resonating valence bonds, spinons and holons
6.4.3 Two-dimensional models
(3b) 2d xy model. Topological excitations (vortices)
6.5 Defects and localized states in magnetic and other systems
7.1 General properties of Fermi systems
7.1.1 Specific heat and susceptibility of free electrons in metals
8 Interacting electrons. Green functions and Feynman diagrams (methods of field theory in many-particle physics)
8.1 Introduction to field-theoretical methods in condensed matter physics
8.2 Representations in quantum mechanics
8.4 Green functions of free (noninteracting) electrons
8.5 Spectral representation of Green functions
8.5.1 Physical meaning of the poles of G(p, w)
8.5.2 Physical meaning of the spectral function A(p, w)
8.6 Phonon Green functions
8.7.1 Dyson equations, self-energy and polarization operators
8.7.2 Effective mass of the electron excitation
9 Electrons with Coulomb interaction
9.1 Dielectric function, screening: random phase approximation
9.2 Nesting and giant Kohn anomalies
9.3 Frequency-dependent dielectric function; dynamic effects
10 Fermi-liquid theory and its generalizations
10.1 The foundations of the Fermi-liquid theory
10.2 Non-Fermi-liquid states
10.2.1 Marginal Fermi liquid
10.2.2 Non-Fermi-liquid close to a quantum critical point
10.2.3 Microscopic mechanisms of non-Fermi-liquid behaviour; Luttinger liquid
11 Instabilities and phase transitions
11.1 Peierls structural transition
11.1.1 Qualitative considerations
11.1.2 Peierls instability in the general case
11.1.3 Different theoretical ways to treat Peierls distortion
11.1.4 Peierls distortion and some of its physical consequences in real systems
11.2 Spin-Peierls transition
11.3 Charge-density waves and structural transitions, higher-dimensional systems
11.4 Excitonic insulators
11.5 Intermezzo: BCS theory of superconductivity
11.7 Different types of CDW and SDW
11.8 Weakly and strongly interacting fermions. Wigner crystallization
12 Strongly correlated electrons
12.3 Magnetic ordering in Mott insulators
12.4 One-particle spectrum of strongly correlated systems
12.4.1 Aproximate treatment (Hubbard I decoupling)
12.4.2 Dealing with Hubbard bands. Spectral weight transfer
12.4.3 Motion of electrons and holes in an antiferromagnetic background
12.5 Ferromagnetism in the Hubbard model?
12.6 Phase diagram of the Hubbard model
12.9 Orbital ordering in the degenerate Hubbard model
12.10 Charge-transfer insulators
12.11 Insulator-metal transition
13 Magnetic impurities in metals, Kondo effect, heavy fermions and mixed valence
13.1 Localized magnetic moments in metals
13.3 Heavy fermion and mixed-valence systems
13.5 Ferromagnetic Kondo lattice and double exchange mechanism of ferromagnetism
Basic Aspects of the Quantum Theory of Solids
：Order and Elementary Excitations
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