From the Preface to the first edition page xiii Preface to the second edition xvii 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 l 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= 5.3.2 d= 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 modeI 6.1 Large-g expansion 6.2 Small-g expansion 6.3 The classical X Y 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 0rder parameter correlations 8.3 The London equation and the superfluid density 8.3.1 The rotor model Exercises 9 Boson Hubbard modeI 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 ⅢNonzero 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，△＞0，T《△ 10.4.2 Low T on the quantum paramagnetic side，△＜0，T《「△」 10.4.3 Continuum high T，T》「△」 10.4.4 Summary 11 Quantum rotor models：large-N Iimit 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＜gf，T《△- 11.4 Numerical studies 12 Thed=1，0(N≥3)rotormodels 12.1 Scaling analysis at zero temperature 12.2 Low-temperature limit of the continuum theory，T《△+ …… Part Ⅳ Other models
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