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 R【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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格式电子书版下载

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Part.Ⅰ Quantum Field Theory1

1．Quantum Mechanics3

1.1 Hilbert Spaces3

1.2 Canonical Formalism4

1.3 Creation and Annihilation Operators6

1.4 Uncertainty Principle10

1.5 CoherentStates andvonNeumannLattice11

1.6 Squeezed Coherent State14

1.7 Particle Number and Phase16

1.8 Macroscopic Coherence18

2．Quantum Field Theory20

2.1 One-Body Hamiltonian20

2.2 Many-Body Hamiltonian21

2.3 Boson Field Operators23

2.4 Quantum Field Theory25

2.5 Fermion Field Operators27

2.6 Electrons Interacting with Electromagnetic Field29

3. Canonical Quantization31

3.1 Relativistic Particles and Wayes31

3.2 Schr？dinger Field32

3.3 Real Klein-Gordon Field37

3.4 Complex Klein-Gordon Field42

3.5 N？ther Currents44

4．Spontaneous Symmetry Breaking47

4.1 Ferromagnets47

4.2 Real Klein-Gordon Field51

4.3 Complex Klein-Gordon Field55

4.4 Sigma Model56

4.5 Schr？dinger Field58

4.6 Superfluidity62

4.7 Goldstone Theorem64

5．Electromagnetic Field67

5.1 Maxwell Equations67

5.2 Canonical Quantization70

5.3 Interaction with Matter Field77

5.4 Anderson-Higgs Mechanism79

5.5 Massive Vector Field81

5.6 Superconductivity83

5.7 Aharonov-Bohm Effect89

6．Dirac Field94

6.1 Dirac Equation94

6.2 Plane Wave Solutions97

6.3 Canonical Quantization99

6.4 Interaction with Electromagnetic Field103

6.5 Weyl Field(Massless Dirac Field)105

6.6 Dirac Electrons in Magnetic Field108

7．Topological Solitons113

7.1 Topological Sectors113

7.2 Classical Fields115

7.3 Solitary Waves,Kinks and Solitons117

7.4 Sine-Gordon Solitons119

7.5 Vortex Solitons123

7.6 Homotopy Classes127

7.7 O(3)Skyrmions132

7.8 CPN-1Skyrmions138

8．Anyons144

8.1 Spin and Statistics144

8.2 Fractional Statistics148

8.3 Quantum Mechanics150

8.4 Chern-Simons Gauge Theory153

8.5 Anyon Field Operators157

Part．Ⅱ Monolayer Quantum Hall Systems161

9．Overview of Monolayer QH Systems163

10．Landau Quantization177

10.1 Planar Electrons177

10.2 Cvclotron Motion181

10.3 Symmetric Gauge187

10.4 Landau Gauge190

10.5 von Neumann Lattice193

10.6 Electrons in Nth Landau Level195

10.7 Hall Current199

11．Quantum Hall Effects204

11.1 Incompressibility204

11.2 Integer Quantum Hall Effects205

11.3 Fractional Quantum Hall Effects207

11.4 Quasiparticles210

11.5 Hall Plateaux213

12．Quasiparticles and Activation Energy215

12.1 Impurity Potentials215

12.2 Gap Energies216

12.3 Dispersion Relation219

12.4 Thermal Activation222

13．Field Theory of Composite Particles227

13.1 Composite Particles227

13.2 Statistical Transmutation230

13.3 Effective Magnetic Field233

13.4 Dressed Composite Particles235

13.5 Composite Particles in Lowest Landau Level239

13.6 Composite Fermions in Lowest Landau Level242

14．Composite Bosons and Semiclassical Analysis246

14.1 GroundState andLaughlinWaveFunction246

14.2 Perturbative Excitations248

14.3 Vortex Excitations250

14.4 Field Theory of Vortex Solitons255

14.5 Haldane-Halperin Hierarchy258

15．Quantum Hall Ferromagnets261

15.1 Spin Coherence261

15.2 Spin Degree of Freedom263

15.3 Composite Bosons and Spin-Charge Separation265

15.4 Spin Field,Sigma Field and CP1 Field268

15.5 Effective Hamiltonian271

16．Spin Textures274

16.1 Spin Excitations274

16.2 Factorizable Skyrmions277

16.3 Skyrmion Excitation Energy284

16.4 Experimental Evidence287

17．Hierarchy of Fractional QH States291

17.1 Jain Hierarchy291

17.2 Landau Levels of Composite Fermions294

17.3 Beyond Principal Sequences296

17.4 Spin Polarization298

17.5 Gap Energies301

18．Edge Effects307

18.1 Edge Currents and Bulk Currents307

18.2 Shot Noises of Fractional Charges308

18.3 Chiral Edge Excitations311

18.4 Chiral Tomonaga-Luttinger Liquid312

18.5 Electrodynamics on Edge316

18.6 EdgeTunneling and Sine-Gordon Solitons320

19．Stripes and Bubbles in Higher Landau Levels325

19.1 Higher Landau Levels325

19.2 Haldane's Pseudopotentials327

19.3 Effective Coulomb Interactions328

19.4 Density Matrix Renormalization Group Method331

19.5 Stripes,Bubbles and Wigner Crystal332

20．Quantum Hall Effects in Graphene335

20.1 Unconventional QH Effects335

20.2 Graphene and Dirac Electrons338

20.3 Dirac Hamiltonian and Supersymmetry343

20.4 Effective Coulomb Interactions346

20.5 Excitonic Condensation352

20.6 Valley Polarization355

20.7 Multilayer Graphene Systems360

20.8 Berry Phase and Index Theorem365

Part.Ⅲ Bilayer Quantum Hall Systems367

21．Overview of Bilayer QH Systems369

22．SU(2)Pseudospin Structure383

22.1 Bilayer Planar Electrons383

22.2 Pseudospins385

22.3 Tunneling Interaction387

22.4 Imbalanced Configuration388

22.5 Capacitance Energy392

22.6 Compound States393

22.7 Charge-Transferable States394

23．Bilayer-Locked States400

23.1 Composite-Boson Field400

23.2 Wave Functions404

23.3 Ground State405

23.4 Vortex Excitations406

24．Interlayer Coherence409

24.1 Pseudospin Ferromagnet409

24.2 Effective Hamiltonian413

24.3 Pseudospin Waves415

24.4 Anomalous Bilayer QH Currents417

24.5 Pseudospin Texture424

25．SU(4)Quantum Hall Ferromagnets428

25.1 SU(4)Isospin Structure428

25.2 SU(4)Isospin Fields431

25.3 SU(4)Isospin Waves433

25.4 SU(4)Isospin Textures436

25.5 ExcitationEnergyofSU(4)Skyrmions440

25.6 Activation Energy Anomaly446

26．Bilayer Quantum Hall Systems atv=2454

26.1 Spin Phase,Ppin Phase and Canted Phase454

26.2 Ground-State Energy457

26.3 Ground-State Structure460

26.4 Phase Diagrams463

26.5 Experimental Data466

26.6 SU(4)Breaking and Grassmannian Fields471

26.7 Grassmannian G42Solitons475

26.8 Genuine Bilayer versus Two-MonolayerSystems479

26.9 Experimental Indication of Biskyrmions482

27．Bilayer Quantum-Hall Junction485

27.1 Josephson-Like Phenomena485

27.2 Parallel Magnetic Field487

27.3 Effective Hamiltonian493

27.4 Commensurate-Incommensurate Phase Transition495

27.5 Soliton Lattice499

27.6 Anomalous Diagonal Resistivity508

27.7 Plasmon Excitations514

27.8 Josephson-Like Effects516

Part.Ⅳ Microscopic Theory521

28．Overview of Microscopic Theory523

29．Noncommutative Geometry534

29.1 Noncommutative Coordinate534

29.2 Weyl Operator and Symbo1535

29.3 Magnetic Translation541

29.4 Density Operators543

29.5 SU(N)-Extended W∞Algebra549

29.6 Classical Fields552

29.7 Topological Charge Density557

29.8 Kac-Moody Algebra on Edges559

30．Landau Level Proj ection562

30.1 Projected Coulomb Interactions562

30.2 Monolayer QH System565

30.3 Electron-Hole Pair Excitations569

30.4 ElectronExcitationandHoleExcitation570

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 Solitons584

31.1 Topological Charge and Electric Charge584

31.2 Microscopic Skyrmion States585

31.3 Noncommutative CP1 Skyrmion589

31.4 Hole and Skyrmion592

31.5 Skyrmion Wave Functions593

31.6 Hardcore Interaction595

31.7 Coulomb Interaction600

31.8 SU(4)Skyrmions605

32．Exchange Interactions and Effective Theory607

32.1 Exchange Hamiltonian607

32.2 Decomposition Formula612

32.3 Spontaneous Symmetry Breaking615

32.4 Classical Equations of Motion616

32.5 Four-Layer Condenser Model618

32.6 Derivative Expansion and Effective Theory622

32.7 Noncommutative CpN-1 Model627

32.8 Equations of Motion and Hall Currents631

32.9 HallCurrentsinPseudospinQHFerromagnet634

Appendices643

A Energy Scales643

B Hausdorff Formulas645

C Group SU(2)and Pauli Matrices647

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

E Cauchy-Riemann Equations650

F Green Function651

G Bogoliubov Transformation652

H Energy-Momentum Tensor654

I Exchange Interaction655

J Mermin-Wagner Theorem659

K Lorentz Transformation663

L One-Dimensional Soliton Solutions666

M Field-Theoretical Vortex Operators669

N Bosonization in One-Dimensional Space672

O Coulomb Energy Formulas677

P Woo Algebra679

References681

Index699