From the Preface to the first edition
Preface to the second edition
Part I Introduction
  1 Basic concepts
    1.1 What is a quantum phase transition?
    1.2 Nonzero temperature transitions and crossovers
    1.3 Experimental examples
    1.4 Theoretical models
      1.4.1 Quantum Ising model
      1.4.2 Quantum rotor model
      1.4.3 Physical realizations of quantum rotors
  2 Overview
    2.1 Quantum field theories
    2.2 What's different about quantum transitions?
Part II A first course
  3 Classical phase transitions
    3.1 Mean-field theory
    3.2 Landau theory
    3.3 Fluctuations and perturbation theory
      3.3.1 Gaussian integrals
      3.3.2 Expansion for susceptibility
    Exercises
  4 The renormalization group
    4.1 Gaussian theory
    4.2 Momentum shell RG
    4.3 Field renormalization
    4.4 Correlation functions
    Exercises
  5 The quantum Ising model
    5.1 Effective Hamiltonian method
    5.2 Large-g expansion
      5.2.1 One-particle states
      5.2.2 Two-particle states
    5.3 Small-g expansion
      5.3.1 d=2
      5.3.2 d=l
    5.4 Review
    5.5 The classical Ising chain
      5.5.1 The scaling limit
      5.5.2 Universality
      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
    Exercises
  6 The quantum rotor model
    6.1 Large-g expansion
    6.2 Small-g 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
      6.6.1 Paramagnet
      6.6.2 Quantum critical point
      6.6.3 Magnetic order
    Exercises
  7 Correlations, susceptibilities, and the quantum critical point
    7.1 Spectral representation
      7.1.1 Structure factor
      7.1.2 Linear response
    7.2 Correlations across the quantum critical point
      7.2.1 Paramagnet
      7.2.2 Quantum critical point
      7.2.3 Magnetic order
    Exercises
  8 Broken symmetries
    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
      8.3.1 The rotor model
      Exercises
  9 Boson Hubbard model
    9.1 Mean-field theory
    9.2 Coherent state path integral
      9.2.1 Boson coherent states
    9.3 Continuum quantum field theories
    Exercises
Part III Nonzero temperatures
  10 The Ising chain in a transverse field
    10.1 Exact spectrum
    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, A > 0, T << A
    10.4.2 Low T on the quantum paramagnetic side, A < 0, T << |△|
    10.4.3 Continuum high T, T >> |△|
    10.4.4 Summary
  11 Quantum rotor models: large-N limit
    11.1 Continuum theory and large-N limit
    11.2 Zero temperature
    11.2.1 Quantum paramagnet, g > gc
    11.2.2 Critical point, g = gc
    11.2.3 Magnetically ordered ground state, g < gc
    11.3 Nonzero temperatures
      11.3.1 Low T on the quantum paramagnetic side, g > gc, T << △+
      11.3.2 High T, T>>△+, △_
      11.3.3 Low T on the magnetically ordered side, g < gc, T << △_
    11.4 Numerical studies
  12 The d = 1, 0(N > 3) rotor models
    12.1 Scaling analysis at zero temperature
    12.2 Low-temperature limit of the continuum theory, T << △+
    12.3 High-temperature limit of the continuum theory, △+ << T << J
      12.3.1 Field-theoretic renormalization group
      12.3.2 Computation of Xu
      12.3.3 Dynamics
    12.4 Summary
  13 The d = 2, 0(N ≥ 3) rotor models
    13.1 Low T on the magnetically ordered side, T << ρs
      13.1.1 Computation of ξc
      13.1.2 Computation of τ
      13.1.3 Structure of correlations
    13.2 Dynamics of the quantum paramagnetic and high-T regions
      13.2.1 Zero temperature
      13.2.2 Nonzero temperatures
    13.3 Summary
  14 Physics dose to and above the upper-critical dimension
    14.1 Zero temperature
      14.1.1 Tricritical crossovers
      14.1.2 Field-theoretic renormalization group
    14.2 Statics at nonzero temperatures
      14.2.1 d < 3
      14.2.2 d > 3
    14.3 Order parameter dynamics in d = 2
    14.4 Applications and extensions
  15 Transport in d = 2
    15.1 Perturbation theory
      15.1.1 σ1
      15.1.2 σ11
    15.2 Collisionless transport equations
    15.3 Collision-dominated transport
      15.3.1 ε expansion
      15.3.2 Large-N limit
    15.4 Physical interpretation
    15.5 The AdS/CFT correspondence
      15.5.1 Exact results for quantum critical transport
      15.5.2 Implications
    15.6 Applications and extensions
Part IV Other models
  16 Dilute Fermi and Bose gases
    16.1 Thequantum XX model
    16.2 The dilute spinless Fermi gas
      16.2.1 Dilute classical gas, kBT << |μ|, μ < 0
      16.2.2 Fermi liquid, kBT <<μ, μ > 0
      16.2.3 High-T limit, kBT >> |μ|
    16.3 The dilute Bose gas
      16.3.1 d < 2
      16.3.2 d = 3
      16.3.3 Correlators of ZB in d = 1
    16.4 The dilute spinful Fermi gas: the Feshbach resonance
      16.4.1 The Fermi-Bose model
      16.4.2 Large-N expansion
    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 Fermi liquid theory
    18.1.1 Independence of choice of k0
    18.2 Ising-nematic ordering
      18.2.1 Hertz theory
      18.2.2 Fate of the fermions
      18.2.3 Non-Fermi liquid criticality in d = 2
    18.3 Spin density wave order
      18.3.1 Mean-field theory
      18.3.2 Continuum theory
      18.3.3 Hertz theory
      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: fetromagnets and antiferromagnets
    19.1 Coherent state path integral
    19.2 Quantized ferromagnets
    19.3 Antiferromagnets
      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 Neel 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 H12
      20.2.1 Sine-Gordon model
      20.2.2 Tomonaga-Luttinger liquid
      20.2.3 Valence bond solid order
      20.2.4 Neel 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
    21.4 Metallic systems
    21.5 Quantum Ising models 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
    21.7 Discussion
    21.8 Applications and extensions
  22 Quantum spin glasses
    22.1 The effective action
      22.1.1 Metallic systems
    22.2 Mean-field theory
    22.3 Applications and extensions
  References
  Index