量子相变 第2版 英文PDF电子书下载

Part Ⅰ Introduction 1

1 Basic concepts 3

1.1 What is a quantum phase transition? 3

1.2 Nonzero temperature transitions and crossovers 5

1.3 Experimental examples 8

1.4 Theoretical models 9

1.4.1 Quantum Ising model 10

1.4.2 Quantum rotor model 12

1.4.3 Physical realizations of quantum rotors 14

2 Overview 18

2.1 Quantum field theories 21

2.2 What's different about quantum transitions? 24

Part Ⅱ A first course 27

3 Classical phase transitions 29

3.1 Mean-field theory 30

3.2 Landau theory 33

3.3 Fluctuations and perturbation theory 34

3.3.1 Gaussian integrals 36

3.3.2 Expansion for susceptibility 39

Exercises 42

4 The renormalization group 45

4.1 Gaussian theory 46

4.2 Momentum shell RG 48

4.3 Field renormalization 53

4.4 Correlation functions 54

Exercises 56

5 The quantum Ising model 58

5.1 Effective Hamiltonian method 58

5.2 Large-g expansion 59

5.2.1 One-particle states 60

5.2.2 Two-particle states 61

5.3 Small-g expansion 64

5.3.1 d=2 64

5.3.2 d=1 66

5.4 Review 67

5.5 The classical Ising chain 67

5.5.1 The scaling limit 70

5.5.2 Universality 71

5.5.3 Mapping to a quantum model:Ising spin in atransversefield 72

5.6 Mapping of the quantum Ising chain to a classical Ising model 74

Exercises 77

6 The quantum rotor model 79

6.1 Large-？expansion 79

6.2 Small-？expansion 80

6.3 The classical X Y chain and an O(2)quantum rotor 82

6.4 The classical Heisenberg chain and an O(3)quantum rotor 88

6.5 Mapping to classical field theories 89

6.6 Spectrum of quantum field theory 90

6.6.1 Paramagnet 91

6.6.2 Quantum critical point 92

6.6.3 Magnetic order 92

Exercises 95

7 Correlations,susceptibilities,and the quantum critical point 96

7.1 Spectral representation 97

7.1.1 Structure factor 98

7.1.2 Linear response 99

7.2 Correlations across the quantum critical point 101

7.2.1 Paramagnet 101

7.2.2 Quantum critical point 103

7.2.3 Magnetic order 104

Exercises 107

8 Broken symmetries 108

8.1 Discrete symmetry and surface tension 108

8.2 Continuous symmetry and the helicity modulus 110

8.2.1 Order parameter correlations 112

8.3 The London equation and the superfluid density 112

8.3.1 The rotor model 115

Exercises 115

9 Boson Hubbard model 117

9.1 Mean-field theory 119

9.2 Coherent state path integral 123

9.2.1 Boson coherent states 125

9.3 Continuum quantum field theories 126

Exercises 130

Part Ⅲ Nonzero temperatures 133

10 The Ising chainin atransversefield 135

10.1 Exact spectrum 137

10.2 Continuum theory and scaling transformations 140

10.3 Equal-time correlations of the order parameter 146

10.4 Finite temperature crossovers 149

10.4.1 Low T on the magnetically ordered side,△＞0,T《△ 151

10.4.2 Low T on the quantum paramagnetic side,△＜0,T《|△| 157

10.4.3 Continuum high T,T》| △| 162

10.4.4 Summary 168

11 Quantum rotor models:large-N limit 171

11.1 Continuum theory and large-N limit 172

11.2 Zero temperature 174

11.2.1 Quantum paramagnet,g＞gc 175

11.2.2 Critical point,g=gc 177

11.2.3 Magnetically ordered ground state,g＜gc 178

11.3 Nonzero temperatures 181

11.3.1 Low T on the quantum paramagnetic side,g＞gc,T《△+ 186

11.3.2 High T,T》△+,△- 186

11.3.3 Low T on the magnetically ordered side,g＜gc,T《△- 187

11.4 Numerical studies 188

12 Thed=1,0(N≥3)rotormodels 190

12.1 Scaling analysis at zero temperature 192

12.2 Low-temperature limit ofthe continuum theory,T《△+ 193

12.3 High-temperature limit of the continuum theory,△+《T《J 199

12.3.1 Field-theoretic renormalization group 201

12.3.2 Computation of xu 205

12.3.3 Dynamics 206

12.4 Summary 211

13 The d=2,0(N≥3)rotor models 213

13.1 Low T on the magnetically ordered side,T《ρs 215

13.1.1 Computation of ξc 216

13.1.2 Computation of τψ 220

13.1.3 Structure of correlations 222

13.2 Dynamics of the quantum paramagnetic and high-T regions 225

13.2.1 Zero temperature 227

13.2.2 Nonzero temperatures 231

13.3 Summary 234

14 Physics close to and above the upper-critical dimension 237

14.1 Zero temperature 239

14.1.1 Tricritical crossovers 239

14.1.2 Field-theoretic renormalization group 240

14.2 Statics at nonzero temperatures 242

14.2.1 d＜3 244

14.2.2 d＞3 248

14.3 Order parameter dynamics in d=2 250

14.4 Applications and extensions 257

15 Transportind=2 260

15.1 Perturbation theory 264

15.1.1 σI 268

15.1.2 σII 269

15.2 Collisionless transport equations 269

15.3 Collision-dominated transport 273

15.3.1 ∈expansion 273

15.3.2 Large-N limit 279

15.4 Physical interpretation 281

15.5 The AdS/CFT correspondence 283

15.5.1 Exact results for quantum critical transport 285

15.5.2 Implications 288

15.6 Applications and extensions 289

Part Ⅳ Other models 291

16 Dilute Fermi and Bose gases 293

16.1 The quantum XX model 296

16.2 The dilute spinless Fermi gas 298

16.2.1 Dilute classical gas,kBT《|μ|,μ＜0 300

16.2.2 Fermi liquid,kBT《μ,μ＞0 301

16.2.3 High-T limit,kBT》|μ| 304

16.3 The dilute Bose gas 305

16.3.1 d＜2 307

16.3.2 d=3 310

16.3.3 Correlators of ZB in d=1 314

16.4 The dilute spinful Fermi gas:the Feshbach resonance 320

16.4.1 The Fermi-Bose model 323

16.4.2 Large-N expansion 327

16.5 Applications and extensions 331

17 Phase transitions of Dirac fermions 332

17.1 d-wave superconductivity and Dirac fermions 332

17.2 Time-reversal symmetry breaking 335

17.3 Field theory and RG analysis 338

17.4 Ising-nematic ordering 342

18 Fermi liquids,and their phase transitions 346

18.1 Fermi liquid theory 347

18.1.1 Independence of choice of？0 354

18.2 Ising-nematic ordering 355

18.2.1 Hertz theory 356

18.2.2 Fate of the fermions 358

18.2.3 Non-Fermi liquid criticality in d=2 360

18.3 Spin density wave order 363

18.3.1 Mean-field theory 364

18.3.2 Continuum theory 365

18.3.3 Hertz theory 367

18.3.4 Fate of the fermions 368

18.3.5 Critical theory in d=2 369

18.4 Nonzero temperature crossovers 370

18.5 Applications and extensions 374

19 Heisenberg spins:ferromagnets and antiferromagnets 375

19.1 Coherent state path integral 375

19.2 Quantized ferromagnets 380

19.3 Antiferromagnets 385

19.3.1 Collinear antiferromagnetism and the quantum nonlinear sigma model 385

19.3.2 Collinear antiferromagnetism in d=1 388

19.3.3 Collinear antiferromagnetism in d=2 390

19.3.4 Noncollinear antiferromagnetism in d=2:deconfined spinons and visons 395

19.3.5 Deconfined criticality 401

19.4 Partial polarization and canted states 403

19.4.1 Quantum paramagnet 405

19.4.2 Quantized ferromagnets 406

19.4.3 Canted and Néel states 406

19.4.4 Zero temperature critical properties 408

19.5 Applications and extensions 410

20 Spin chains:bosonization 412

20.1 The XX chain revisited:bosonization 413

20.2 Phases of H12 423

20.2.1 Sine-Gordon model 425

20.2.2 Tomonaga-Luttinger liquid 428

20.2.3 Valence bond solid order 428

20.2.4 Néel order 431

20.2.5 Models with SU(2)(Heisenberg)symmetry 431

20.2.6 Critical properties near phase boundaries 433

20.3 O(2)rotor modelin d=1 435

20.4 Applications and extensions 436

21 Magnetic ordering transitions of disordered systems 437

21.1 Stability of quantum critical points in disordered systems 438

21.2 Griffiths-McCoy singularities 440

21.3 Perturbative field-theoretic analysis 442

21.4 Metallic systems 445

21.5 Quantum lsing models near the percolation transition 447

21.5.1 Percolation theory 447

21.5.2 Classieal dilute Ising models 448

21.5.3 Quantum dilute Ising models 449

21.6 The disordered quantum Ising chain 453

21.7 Discussion 460

21.8 Applications and extensions 461

22 Quantum spin glasses 463

22.1 The effective action 464

22.1.1 Metallic systems 469

22.2 Mean-feld theory 470

22.3 Applications and extensions 477

References 479

Index 496