量子相变 第2版 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

量子相变 第2版 英文PDF格式电子书版下载

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Part Ⅰ Introduction1

1 Basic concepts3

1.1 What is a quantum phase transition?3

1.2 Nonzero temperature transitions and crossovers5

1.3 Experimental examples8

1.4 Theoretical models9

1.4.1 Quantum Ising model10

1.4.2 Quantum rotor model12

1.4.3 Physical realizations of quantum rotors14

2 Overview18

2.1 Quantum field theories21

2.2 What's different about quantum transitions?24

Part Ⅱ A first course27

3 Classical phase transitions29

3.1 Mean-field theory30

3.2 Landau theory33

3.3 Fluctuations and perturbation theory34

3.3.1 Gaussian integrals36

3.3.2 Expansion for susceptibility39

Exercises42

4 The renormalization group45

4.1 Gaussian theory46

4.2 Momentum shell RG48

4.3 Field renormalization53

4.4 Correlation functions54

Exercises56

5 The quantum Ising model58

5.1 Effective Hamiltonian method58

5.2 Large-g expansion59

5.2.1 One-particle states60

5.2.2 Two-particle states61

5.3 Small-g expansion64

5.3.1 d=264

5.3.2 d=166

5.4 Review67

5.5 The classical Ising chain67

5.5.1 The scaling limit70

5.5.2 Universality71

5.5.3 Mapping to a quantum model:Ising spin in atransversefield72

5.6 Mapping of the quantum Ising chain to a classical Ising model74

Exercises77

6 The quantum rotor model79

6.1 Large-？expansion79

6.2 Small-？expansion80

6.3 The classical X Y chain and an O(2)quantum rotor82

6.4 The classical Heisenberg chain and an O(3)quantum rotor88

6.5 Mapping to classical field theories89

6.6 Spectrum of quantum field theory90

6.6.1 Paramagnet91

6.6.2 Quantum critical point92

6.6.3 Magnetic order92

Exercises95

7 Correlations,susceptibilities,and the quantum critical point96

7.1 Spectral representation97

7.1.1 Structure factor98

7.1.2 Linear response99

7.2 Correlations across the quantum critical point101

7.2.1 Paramagnet101

7.2.2 Quantum critical point103

7.2.3 Magnetic order104

Exercises107

8 Broken symmetries108

8.1 Discrete symmetry and surface tension108

8.2 Continuous symmetry and the helicity modulus110

8.2.1 Order parameter correlations112

8.3 The London equation and the superfluid density112

8.3.1 The rotor model115

Exercises115

9 Boson Hubbard model117

9.1 Mean-field theory119

9.2 Coherent state path integral123

9.2.1 Boson coherent states125

9.3 Continuum quantum field theories126

Exercises130

Part Ⅲ Nonzero temperatures133

10 The Ising chainin atransversefield135

10.1 Exact spectrum137

10.2 Continuum theory and scaling transformations140

10.3 Equal-time correlations of the order parameter146

10.4 Finite temperature crossovers149

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 Summary168

11 Quantum rotor models:large-N limit171

11.1 Continuum theory and large-N limit172

11.2 Zero temperature174

11.2.1 Quantum paramagnet,g＞gc175

11.2.2 Critical point,g=gc177

11.2.3 Magnetically ordered ground state,g＜gc178

11.3 Nonzero temperatures181

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 studies188

12 Thed=1,0(N≥3)rotormodels190

12.1 Scaling analysis at zero temperature192

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

12.3 High-temperature limit of the continuum theory,△+《T《J199

12.3.1 Field-theoretic renormalization group201

12.3.2 Computation of xu205

12.3.3 Dynamics206

12.4 Summary211

13 The d=2,0(N≥3)rotor models213

13.1 Low T on the magnetically ordered side,T《ρs215

13.1.1 Computation of ξc216

13.1.2 Computation of τψ220

13.1.3 Structure of correlations222

13.2 Dynamics of the quantum paramagnetic and high-T regions225

13.2.1 Zero temperature227

13.2.2 Nonzero temperatures231

13.3 Summary234

14 Physics close to and above the upper-critical dimension237

14.1 Zero temperature239

14.1.1 Tricritical crossovers239

14.1.2 Field-theoretic renormalization group240

14.2 Statics at nonzero temperatures242

14.2.1 d＜3244

14.2.2 d＞3248

14.3 Order parameter dynamics in d=2250

14.4 Applications and extensions257

15 Transportind=2260

15.1 Perturbation theory264

15.1.1 σI268

15.1.2 σII269

15.2 Collisionless transport equations269

15.3 Collision-dominated transport273

15.3.1 ∈expansion273

15.3.2 Large-N limit279

15.4 Physical interpretation281

15.5 The AdS/CFT correspondence283

15.5.1 Exact results for quantum critical transport285

15.5.2 Implications288

15.6 Applications and extensions289

Part Ⅳ Other models291

16 Dilute Fermi and Bose gases293

16.1 The quantum XX model296

16.2 The dilute spinless Fermi gas298

16.2.1 Dilute classical gas,kBT《|μ|,μ＜0300

16.2.2 Fermi liquid,kBT《μ,μ＞0301

16.2.3 High-T limit,kBT》|μ|304

16.3 The dilute Bose gas305

16.3.1 d＜2307

16.3.2 d=3310

16.3.3 Correlators of ZB in d=1314

16.4 The dilute spinful Fermi gas:the Feshbach resonance320

16.4.1 The Fermi-Bose model323

16.4.2 Large-N expansion327

16.5 Applications and extensions331

17 Phase transitions of Dirac fermions332

17.1 d-wave superconductivity and Dirac fermions332

17.2 Time-reversal symmetry breaking335

17.3 Field theory and RG analysis338

17.4 Ising-nematic ordering342

18 Fermi liquids,and their phase transitions346

18.1 Fermi liquid theory347

18.1.1 Independence of choice of？0354

18.2 Ising-nematic ordering355

18.2.1 Hertz theory356

18.2.2 Fate of the fermions358

18.2.3 Non-Fermi liquid criticality in d=2360

18.3 Spin density wave order363

18.3.1 Mean-field theory364

18.3.2 Continuum theory365

18.3.3 Hertz theory367

18.3.4 Fate of the fermions368

18.3.5 Critical theory in d=2369

18.4 Nonzero temperature crossovers370

18.5 Applications and extensions374

19 Heisenberg spins:ferromagnets and antiferromagnets375

19.1 Coherent state path integral375

19.2 Quantized ferromagnets380

19.3 Antiferromagnets385

19.3.1 Collinear antiferromagnetism and the quantum nonlinear sigma model385

19.3.2 Collinear antiferromagnetism in d=1388

19.3.3 Collinear antiferromagnetism in d=2390

19.3.4 Noncollinear antiferromagnetism in d=2:deconfined spinons and visons395

19.3.5 Deconfined criticality401

19.4 Partial polarization and canted states403

19.4.1 Quantum paramagnet405

19.4.2 Quantized ferromagnets406

19.4.3 Canted and Néel states406

19.4.4 Zero temperature critical properties408

19.5 Applications and extensions410

20 Spin chains:bosonization412

20.1 The XX chain revisited:bosonization413

20.2 Phases of H12423

20.2.1 Sine-Gordon model425

20.2.2 Tomonaga-Luttinger liquid428

20.2.3 Valence bond solid order428

20.2.4 Néel order431

20.2.5 Models with SU(2)(Heisenberg)symmetry431

20.2.6 Critical properties near phase boundaries433

20.3 O(2)rotor modelin d=1435

20.4 Applications and extensions436

21 Magnetic ordering transitions of disordered systems437

21.1 Stability of quantum critical points in disordered systems438

21.2 Griffiths-McCoy singularities440

21.3 Perturbative field-theoretic analysis442

21.4 Metallic systems445

21.5 Quantum lsing models near the percolation transition447

21.5.1 Percolation theory447

21.5.2 Classieal dilute Ising models448

21.5.3 Quantum dilute Ising models449

21.6 The disordered quantum Ising chain453

21.7 Discussion460

21.8 Applications and extensions461

22 Quantum spin glasses463

22.1 The effective action464

22.1.1 Metallic systems469

22.2 Mean-feld theory470

22.3 Applications and extensions477

References479

Index496