量子相变

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

《量子相变（第2版）（英文版）》讲述量子相变是物质的量子相在零温下的一种相变。相比于经典相变，量子相变可以仅通过在绝对零度下改变一些物理参数（如磁场或压力）就可以实现。量子相变描述量子涨落导致的多体系统基态的突变，这可以是一个二级相变。在相变现象中，大量微观粒子的相互作用与热或量子涨落的竞争起到核心的作用，而相变的行为通常具有普适性，又与相互作用的细节无关。