量子霍尔效应 场论方法与相关主题 第2版 影印版=QUANTUM HALL EFFECTS FIELD THEORETICAL APPROACH AND RELATED TOPICS AND RPDF电子书下载

Part.Ⅰ Quantum Field Theory 1

1．Quantum Mechanics 3

1.1 Hilbert Spaces 3

1.2 Canonical Formalism 4

1.3 Creation and Annihilation Operators 6

1.4 Uncertainty Principle 10

1.5 CoherentStates andvonNeumannLattice 11

1.6 Squeezed Coherent State 14

1.7 Particle Number and Phase 16

1.8 Macroscopic Coherence 18

2．Quantum Field Theory 20

2.1 One-Body Hamiltonian 20

2.2 Many-Body Hamiltonian 21

2.3 Boson Field Operators 23

2.4 Quantum Field Theory 25

2.5 Fermion Field Operators 27

2.6 Electrons Interacting with Electromagnetic Field 29

3. Canonical Quantization 31

3.1 Relativistic Particles and Wayes 31

3.2 Schr？dinger Field 32

3.3 Real Klein-Gordon Field 37

3.4 Complex Klein-Gordon Field 42

3.5 N？ther Currents 44

4．Spontaneous Symmetry Breaking 47

4.1 Ferromagnets 47

4.2 Real Klein-Gordon Field 51

4.3 Complex Klein-Gordon Field 55

4.4 Sigma Model 56

4.5 Schr？dinger Field 58

4.6 Superfluidity 62

4.7 Goldstone Theorem 64

5．Electromagnetic Field 67

5.1 Maxwell Equations 67

5.2 Canonical Quantization 70

5.3 Interaction with Matter Field 77

5.4 Anderson-Higgs Mechanism 79

5.5 Massive Vector Field 81

5.6 Superconductivity 83

5.7 Aharonov-Bohm Effect 89

6．Dirac Field 94

6.1 Dirac Equation 94

6.2 Plane Wave Solutions 97

6.3 Canonical Quantization 99

6.4 Interaction with Electromagnetic Field 103

6.5 Weyl Field(Massless Dirac Field) 105

6.6 Dirac Electrons in Magnetic Field 108

7．Topological Solitons 113

7.1 Topological Sectors 113

7.2 Classical Fields 115

7.3 Solitary Waves,Kinks and Solitons 117

7.4 Sine-Gordon Solitons 119

7.5 Vortex Solitons 123

7.6 Homotopy Classes 127

7.7 O(3)Skyrmions 132

7.8 CPN-1Skyrmions 138

8．Anyons 144

8.1 Spin and Statistics 144

8.2 Fractional Statistics 148

8.3 Quantum Mechanics 150

8.4 Chern-Simons Gauge Theory 153

8.5 Anyon Field Operators 157

Part．Ⅱ Monolayer Quantum Hall Systems 161

9．Overview of Monolayer QH Systems 163

10．Landau Quantization 177

10.1 Planar Electrons 177

10.2 Cvclotron Motion 181

10.3 Symmetric Gauge 187

10.4 Landau Gauge 190

10.5 von Neumann Lattice 193

10.6 Electrons in Nth Landau Level 195

10.7 Hall Current 199

11．Quantum Hall Effects 204

11.1 Incompressibility 204

11.2 Integer Quantum Hall Effects 205

11.3 Fractional Quantum Hall Effects 207

11.4 Quasiparticles 210

11.5 Hall Plateaux 213

12．Quasiparticles and Activation Energy 215

12.1 Impurity Potentials 215

12.2 Gap Energies 216

12.3 Dispersion Relation 219

12.4 Thermal Activation 222

13．Field Theory of Composite Particles 227

13.1 Composite Particles 227

13.2 Statistical Transmutation 230

13.3 Effective Magnetic Field 233

13.4 Dressed Composite Particles 235

13.5 Composite Particles in Lowest Landau Level 239

13.6 Composite Fermions in Lowest Landau Level 242

14．Composite Bosons and Semiclassical Analysis 246

14.1 GroundState andLaughlinWaveFunction 246

14.2 Perturbative Excitations 248

14.3 Vortex Excitations 250

14.4 Field Theory of Vortex Solitons 255

14.5 Haldane-Halperin Hierarchy 258

15．Quantum Hall Ferromagnets 261

15.1 Spin Coherence 261

15.2 Spin Degree of Freedom 263

15.3 Composite Bosons and Spin-Charge Separation 265

15.4 Spin Field,Sigma Field and CP1 Field 268

15.5 Effective Hamiltonian 271

16．Spin Textures 274

16.1 Spin Excitations 274

16.2 Factorizable Skyrmions 277

16.3 Skyrmion Excitation Energy 284

16.4 Experimental Evidence 287

17．Hierarchy of Fractional QH States 291

17.1 Jain Hierarchy 291

17.2 Landau Levels of Composite Fermions 294

17.3 Beyond Principal Sequences 296

17.4 Spin Polarization 298

17.5 Gap Energies 301

18．Edge Effects 307

18.1 Edge Currents and Bulk Currents 307

18.2 Shot Noises of Fractional Charges 308

18.3 Chiral Edge Excitations 311

18.4 Chiral Tomonaga-Luttinger Liquid 312

18.5 Electrodynamics on Edge 316

18.6 EdgeTunneling and Sine-Gordon Solitons 320

19．Stripes and Bubbles in Higher Landau Levels 325

19.1 Higher Landau Levels 325

19.2 Haldane's Pseudopotentials 327

19.3 Effective Coulomb Interactions 328

19.4 Density Matrix Renormalization Group Method 331

19.5 Stripes,Bubbles and Wigner Crystal 332

20．Quantum Hall Effects in Graphene 335

20.1 Unconventional QH Effects 335

20.2 Graphene and Dirac Electrons 338

20.3 Dirac Hamiltonian and Supersymmetry 343

20.4 Effective Coulomb Interactions 346

20.5 Excitonic Condensation 352

20.6 Valley Polarization 355

20.7 Multilayer Graphene Systems 360

20.8 Berry Phase and Index Theorem 365

Part.Ⅲ Bilayer Quantum Hall Systems 367

21．Overview of Bilayer QH Systems 369

22．SU(2)Pseudospin Structure 383

22.1 Bilayer Planar Electrons 383

22.2 Pseudospins 385

22.3 Tunneling Interaction 387

22.4 Imbalanced Configuration 388

22.5 Capacitance Energy 392

22.6 Compound States 393

22.7 Charge-Transferable States 394

23．Bilayer-Locked States 400

23.1 Composite-Boson Field 400

23.2 Wave Functions 404

23.3 Ground State 405

23.4 Vortex Excitations 406

24．Interlayer Coherence 409

24.1 Pseudospin Ferromagnet 409

24.2 Effective Hamiltonian 413

24.3 Pseudospin Waves 415

24.4 Anomalous Bilayer QH Currents 417

24.5 Pseudospin Texture 424

25．SU(4)Quantum Hall Ferromagnets 428

25.1 SU(4)Isospin Structure 428

25.2 SU(4)Isospin Fields 431

25.3 SU(4)Isospin Waves 433

25.4 SU(4)Isospin Textures 436

25.5 ExcitationEnergyofSU(4)Skyrmions 440

25.6 Activation Energy Anomaly 446

26．Bilayer Quantum Hall Systems atv=2 454

26.1 Spin Phase,Ppin Phase and Canted Phase 454

26.2 Ground-State Energy 457

26.3 Ground-State Structure 460

26.4 Phase Diagrams 463

26.5 Experimental Data 466

26.6 SU(4)Breaking and Grassmannian Fields 471

26.7 Grassmannian G42Solitons 475

26.8 Genuine Bilayer versus Two-MonolayerSystems 479

26.9 Experimental Indication of Biskyrmions 482

27．Bilayer Quantum-Hall Junction 485

27.1 Josephson-Like Phenomena 485

27.2 Parallel Magnetic Field 487

27.3 Effective Hamiltonian 493

27.4 Commensurate-Incommensurate Phase Transition 495

27.5 Soliton Lattice 499

27.6 Anomalous Diagonal Resistivity 508

27.7 Plasmon Excitations 514

27.8 Josephson-Like Effects 516

Part.Ⅳ Microscopic Theory 521

28．Overview of Microscopic Theory 523

29．Noncommutative Geometry 534

29.1 Noncommutative Coordinate 534

29.2 Weyl Operator and Symbo1 535

29.3 Magnetic Translation 541

29.4 Density Operators 543

29.5 SU(N)-Extended W∞Algebra 549

29.6 Classical Fields 552

29.7 Topological Charge Density 557

29.8 Kac-Moody Algebra on Edges 559

30．Landau Level Proj ection 562

30.1 Projected Coulomb Interactions 562

30.2 Monolayer QH System 565

30.3 Electron-Hole Pair Excitations 569

30.4 ElectronExcitationandHoleExcitation 570

30.5 Bilayer System withoutSpin(v=1) 573

30.6 Bilayer System with Spin(v=1) 575

30.7 Bilayer System with Spins(v=2) 578

31．Noncommutative Solitons 584

31.1 Topological Charge and Electric Charge 584

31.2 Microscopic Skyrmion States 585

31.3 Noncommutative CP1 Skyrmion 589

31.4 Hole and Skyrmion 592

31.5 Skyrmion Wave Functions 593

31.6 Hardcore Interaction 595

31.7 Coulomb Interaction 600

31.8 SU(4)Skyrmions 605

32．Exchange Interactions and Effective Theory 607

32.1 Exchange Hamiltonian 607

32.2 Decomposition Formula 612

32.3 Spontaneous Symmetry Breaking 615

32.4 Classical Equations of Motion 616

32.5 Four-Layer Condenser Model 618

32.6 Derivative Expansion and Effective Theory 622

32.7 Noncommutative CpN-1 Model 627

32.8 Equations of Motion and Hall Currents 631

32.9 HallCurrentsinPseudospinQHFerromagnet 634

Appendices 643

A Energy Scales 643

B Hausdorff Formulas 645

C Group SU(2)and Pauli Matrices 647

D Groups SU(N)and SU(2N) 647

E Cauchy-Riemann Equations 650

F Green Function 651

G Bogoliubov Transformation 652

H Energy-Momentum Tensor 654

I Exchange Interaction 655

J Mermin-Wagner Theorem 659

K Lorentz Transformation 663

L One-Dimensional Soliton Solutions 666

M Field-Theoretical Vortex Operators 669

N Bosonization in One-Dimensional Space 672

O Coulomb Energy Formulas 677

P Woo Algebra 679

References 681

Index 699