Chapter
3.3 Fluctuations and perturbation theory
3.3.2 Expansion for susceptibility
4 The renormalization group
4.3 Field renormalization
4.4 Correlation functions
5 The quantum Ising model
5.1 Effective Hamiltonian method
5.2.1 One-particle states
5.2.2 Two-particle states
5.5 The classical Ising chain
5.5.3 Mapping to a quantum model: Ising spin in a transverse field
5.6 Mapping of the quantum Ising chain to a classical Ising model
6 The quantum rotor model
6.1 Large-g[tilde]
expansion
6.2 Small-g[tilde]
expansion
6.3 The classical XY chain and an O(2) quantum rotor
6.4 The classical Heisenberg chain and an O(3) quantum rotor
6.5 Mapping to classical field theories
6.6 Spectrum of quantum field theory
6.6.2 Quantum critical point
7 Correlations, susceptibilities, and the quantum critical point
7.1 Spectral representation
7.2 Correlations across the quantum critical point
7.2.2 Quantum critical point
8.1 Discrete symmetry and surface tension
8.2 Continuous symmetry and the helicity modulus
8.2.1 Order parameter correlations
8.3 The London equation and the superfluid density
9.2 Coherent state path integral
9.2.1 Boson coherent states
9.3 Continuum quantum field theories
Part III Nonzero temperatures
10 The Ising chain in a transverse field
10.2 Continuum theory and scaling transformations
10.3 Equal-time correlations of the order parameter
10.4 Finite temperature crossovers
10.4.1 Low T on the magnetically ordered side,
∆ > 0, T << ∆
10.4.2 Low T on the quantum paramagnetic side, ∆< 0, T << |∆|
10.4.3 Continuum high T, T >> |∆|
11 Quantum rotor models: large-N limit
11.1 Continuum theory and large-N limit
11.2.1 Quantum paramagnet, g > g[sub(c)]
11.2.2 Critical point, g = g[sub(c)]
11.2.3 Magnetically ordered ground state, g < g[sub(c)]
11.3 Nonzero temperatures
11.3.1 Low T on the quantum paramagnetic side, g > g[sub(c)], T << ∆[sub(+)]
11.3.2 High T, T >> ∆[sub(+)], ∆[sub(_)]
11.3.3 Low T on the magnetically ordered side, g < g[sub(c)], T << ∆[sub(_)]
12 The d =1,O(N≥3) rotor models
12.1 Scaling analysis at zero temperature
12.2 Low-temperature limit of the continuum theory, T << ∆[sub(+)]
12.3 High-temperature limit of the continuum theory, ∆[sub(+)] << T << J
12.3.1 Field-theoretic renormalization group
12.3.2 Computation of χ[sub(u)]
13 The d=2, O(N≥3) rotor models
13.1 Low T on the magnetically ordered side, T << ρ[sub(s)]
13.1.1 Computation of ξ[sub(c)]
13.1.2 Computation of τ[sub(φ)]
13.1.3 Structure of correlations
13.2 Dynamics of the quantum paramagnetic and high-T regions
13.2.2 Nonzero temperatures
14 Physics close to and above the upper-critical dimension
14.1.1 Tricritical crossovers
14.1.2 Field-theoretic renormalization group
14.2 Statics at nonzero temperatures
14.3 Order parameter dynamics in d = 2
14.4 Applications and extensions
15.2 Collisionless transport equations
15.3 Collision-dominated transport
15.4 Physical interpretation
15.5 The AdS/CFT correspondence
15.5.1 Exact results for quantum critical transport
15.6 Applications and extensions
16 Dilute Fermi and Bose gases
16.1 The quantum XX model
16.2 The dilute spinless Fermi gas
16.2.1 Dilute classical gas, k[sub(B)]T << |µ|, µ < 0
16.2.2 Fermi liquid, k[sub(B)]T << µ, µ > 0
16.2.3 High-T limit, k[sub(B)]T >> |µ|
16.3.3 Correlators of Z[sub(B)] in d = 1
16.4 The dilute spinful Fermi gas: the Feshbach resonance
16.4.1 The Fermi–Bose model
16.5 Applications and extensions
17 Phase transitions of Dirac fermions
17.1 d-wave superconductivity and Dirac fermions
17.2 Time-reversal symmetry breaking
17.3 Field theory and RG analysis
17.4 Ising-nematic ordering
18 Fermi liquids, and their phase transitions
18.1.1 Independence of choice of k[arrow][sub(0)]
18.2 Ising-nematic ordering
18.2.2 Fate of the fermions
18.2.3 Non-Fermi liquid criticality in d = 2
18.3 Spin density wave order
18.3.4 Fate of the fermions
18.3.5 Critical theory in d = 2
18.4 Nonzero temperature crossovers
18.5 Applications and extensions
19 Heisenberg spins: ferromagnets and antiferromagnets
19.1 Coherent state path integral
19.2 Quantized ferromagnets
19.3.1 Collinear antiferromagnetism and the quantum nonlinear sigma model
19.3.2 Collinear antiferromagnetism in d = 1
19.3.3 Collinear antiferromagnetism in d = 2
19.3.4 Noncollinear antiferromagnetism in d = 2: deconfined spinons and visons
19.3.5 Deconfined criticality
19.4 Partial polarization and canted states
19.4.1 Quantum paramagnet
19.4.2 Quantized ferromagnets
19.4.3 Canted and Néel states
19.4.4 Zero temperature critical properties
19.5 Applications and extensions
20 Spin chains: bosonization
20.1 The XX chain revisited: bosonization
20.2 Phases of H[sub(12)]
20.2.2 Tomonaga–Luttinger liquid
20.2.3 Valence bond solid order
20.2.5 Models with SU(2) (Heisenberg) symmetry
20.2.6 Critical properties near phase boundaries
20.3 O(2) rotor model in d = 1
20.4 Applications and extensions
21 Magnetic ordering transitions of disordered systems
21.1 Stability of quantum critical points in disordered systems
21.2 Griffiths–McCoy singularities
21.3 Perturbative field-theoretic analysis
21.5 Quantum Isingmodels near the percolation transition
21.5.1 Percolation theory
21.5.2 Classical dilute Ising models
21.5.3 Quantum dilute Ising models
21.6 The disordered quantum Ising chain
21.8 Applications and extensions
22.1 The effective action
22.3 Applications and extensions
Quantum Phase Transitions
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