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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£ºIsing 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 ¢óNonzero 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£¬¡÷£¾0£¬T¡¶¡÷
10.4.2 Low T on the quantum paramagnetic side£¬¡÷£¼0£¬T¡¶¡¸¡÷¡¹
10.4.3 Continuum high T£¬T¡·¡¸¡÷¡¹
10.4.4 Summary
11 Quantum rotor models£ºlarge-N Iimit
11.1 Continuum theory and large-N limit
11.2 Zero temperature
11.2.1 Quantum paramagnet£¬g£¾gc
11.2.2 Critical point£¬g=gc
11.2.3 Magnetically ordered ground state£¬g£¼gc
11.3 Nonzero temperatures
11.3.1 Low T on the quantum paramagnetic side£¬g£¾gc£¬T¡¶¡÷+
11.3.2 High T£¬T¡·¡÷+£¬¡÷-
11.3.3 Low T on the magnetically ordered side£¬g£¼gf£¬T¡¶¡÷-
11.4 Numerical studies
12 Thed=1£¬0(N¡Ý3)rotormodels
12.1 Scaling analysis at zero temperature
12.2 Low-temperature limit of the continuum theory£¬T¡¶¡÷+
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Part ¢ô Other models