电子关联和磁性 英文PDF电子书下载

1 Introduction 1

1.1 Magnetism and Other Effects of Electron-Electron Inter-action 1

1.2 Sources of Magnetic Fields 5

1.3 Getting Acquainted:Magnetite 7

1.3.1 Charge States 8

1.3.2 Spin States 9

1.3.3 Charge Ordering 11

1.4 Variety of Correlated Systems:An Outline of the Course 14

2 Atoms,Ions,and Molecules 17

2.1 Hydrogen Atom in a Magnetic Field 18

2.1.1 Non-Relativistic Treatment 18

Motion in a Magnetic Field 19

Zeeman Effect（Ⅰ） 21

2.1.2 Relativistic Effects 22

Spin-Orbit Coupling 24

Zeeman Effect （Ⅱ） 25

Problem 2.1 28

2.2 Direct Exchange 28

Problem 2.2 36

2.3 Many-Electron Ions 36

Problem 2.3 40

2.3.1 Coupling to the Magnetic Field 40

Digression:The Bohr-Van Leeuwen Theorem 42

2.3.2 Hund's Rules 43

Problem 2.4 45

2.4 Paramagnetism and Diamagnetism 45

2.4.1 Paramagnetic Susceptibility 46

Magnetization Curve 51

Problems 2.5-2.8 52

2.4.2 Diamagnetism 53

Digression:Superstrong Fields 54

2.5 Hydrogen Molecule 56

2.5.1 Direct Exchange in Non-Orthogonal Orbitals 57

2.5.2 Kinetic Exchange 60

2.5.3 Molecular Orbitals versus Heitler-London 64

Solutions to the Problems 66

3 Crystal Field Theory 75

3.1 Incomplete Shells in an Anisotropic Environment:Crys-tal Fields 75

3.2 The Role of Symmetry Arguments in Quantum Mechanics 80

3.2.1 Irreducible Representations 82

3.3 The Octahedral Group 86

Problems 3.1-3.2 89

3.4 Symmetry Properties of Atomic States 89

3.5 Splitting of a d-Level in Cubic Field 91

3.5.1 Quenching the Orbital Angular Momentum 94

3.5.2 Partial Restoration of Orbital Momentum by Spin Orbit Coupling 96

Problems 3.3-3.4 98

3.5.3 High-Spin versus Low-Spin States 98

3.6 Jahn-Teller Effect 100

3.7 Time Reversal Invariance 104

3.8 The f2 Configuration 110

3.8.1 Cubic Crystal Field 111

3.8.2 Tetragonal Crystal Field 115

3.8.3 Metamagnetic Transition 118

3.8.4 Exchange Induced Magnetism 121

Problems 3.5-3.6 122

3.9 Double Groups 122

Problems 3.7-3.8 128

3.10 Crystal Field Potentials 128

3.10.1 Quadrupole Moments 132

Solutions to the Problems 134

4 Mott Transition and Hubbard Model 147

4.1 Metals and Insulators:Breakdown of the Independent-Electron Description 147

4.2 Mott Transition 150

4.3 The Hubbard Model 157

4.3.1 Local Basis 161

4.3.2 Which Electrons Do We Mean? 162

4.4 Limiting Cases 163

4.4.1 The Band Limit 164

Problems 4.1-4.4 166

4.4.2 The Atomic Limit 167

What Causes the Ordering? 169

4.5 Symmetries 170

4.5.1 Spin-Rotational Invariance 170

4.5.2 Electron-Hole Symmetry 171

Problem 4.5 173

4.6 Infinite-Dimensional Hubbard Model 173

Problems 4.6-4.8 177

4.7 Hubbard Subbands 178

4.7.1 The Mott-Hubbard Transition 180

4.8 Ground State Phase Diagram 182

Solutions to the Problems 187

5 Mott Insulators 199

5.1 The Large-U Limit 199

5.1.1 Classification of Hopping Events 200

5.1.2 The Canonical Transformation 203

5.1.3 Hubbard Operators 205

5.1.4 The t-J Model 207

5.1.5 Half-Filled Band:The Heisenberg Model 211

Problems 5.1-5.2 213

5.1.6 Higher-Order Exchange 214

5.2 Superexchange 217

5.3 The Extended Hubbard Model 221

Problems 5.3-5.5 226

5.4 Orbital Degeneracy,Orbital Ordering 226

Problems 5.6-5.8 234

5.5 Correlated Insulators 234

5.5.1 Mott Transitions in Transition Metal Oxides 235

5.5.2 Mott Insulators versus Charge Transfer Insulators 243

Hole Doping 248

Solutions to the Problems 250

6 Heisenberg Magnets 263

6.1 Ferromagnetic Heisenberg Model 264

6.1.1 Ground State:Symmetry Breaking 265

6.1.2 Excitations:Spin Waves 268

Effects of Anisotropy 275

Magnon-Magnon Interactions 276

Finite Temperatures 277

Problem 6.1 279

6.2 Antiferromagnetic Heisenberg Model 280

6.2.1 Introduction 280

6.2.2 Spin Waves 283

Sublattice Magnetization 290

Anisotropy 297

A Glimpse at the Strange World of D=1 299

6.3 Néel Order versus Valence Bond States 306

6.3.1 Resonating Valence Bonds 307

Problems 6.2-6.4 311

Digression:Symmetry Breaking 312

6.3.2 Valence Bond Solids 315

6.3.3 The CaV4O9 Story 326

6.3.4 Frustration 330

Problem 6.5 335

Solutions to the Problems 336

7 Itinerant Electron Magnetism 341

7.1 Introduction 341

7.2 Magnetic Order 344

7.2.1 Digression:Symmetry Breaking 347

7.3 Mean Field Theories 349

7.4 Stoner Model 352

Problems 7.1-7.3 357

7.5 Generalized Susceptibility 357

7.5.1 Criteria for q≠0 Instabilities 360

Problems 7.4-7.5 362

7.6 Spin Density Waves 363

7.6.1 Gap Equation 367

7.6.2 Finite Temperatures 370

7.6.3 Strong Coupling Limit 376

7.6.4 Away from Half-Filling 381

Problems 7.6-7.9 385

7.7 Transition Metals and Alloys 386

7.7.1 Introduction 386

7.7.2 LSDA versus Lattice Fermion Models 389

7.7.3 Nearly Ferromagnetic Metals 394

7.7.4 Ferromagnetic Metals 396

Weak Itinerant Ferromagnets 396

Iron Group Elements 399

Paramagnetic Susceptibility 401

7.7.5 Chromium 402

Solutions to the Problems 406

8 Ferromagnetism in Hubbard Models 419

8.1 Preliminary Overview 419

8.1.1 The Low-Density Limit 423

8.2 Exactly Proven Cases of High-Spin Ground States 425

8.2.1 Lieb's Ferrimagnetism 426

8.2.2 Flat-Band Ferromagnetism 428

8.2.3 Nagaoka Ferromagnetism 430

Probem 8.1 433

8.2.4 Ferromagnetism in a Nearly Flat Band 433

8.3 The Ring Exchange Mechanism 435

Probem 8.2 440

8.4 Instability of the Nagaoka State 441

8.4.1 The Single-Spin-Flip State 442

8.4.2 Improved Variational Methods:Square Lattice 448

8.4.3 Lattice Structure Dependence of Ferromagnetism in a Single-Band Model 451

The fcc Lattice 455

Discussion 458

8.5 Effects of Degeneracy 463

8.5.1 Double Exchange 463

Problem 8.3 470

8.5.2 Two-Band Model 470

8.5.3 The LaMnO3 System 473

Magnetostructural Transition 478

Charge Ordering 480

Solutions to the Problems 485

9 The Gutzwiller Variational Method 497

9.1 Minimum Polarity Principle 499

9.1.1 Digression:The Early History 502

9.2 The Variational Ground State 505

9.2.1 The Gutzwiller Trial State 506

Problems 9.1-9.2 513

9.2.2 The Cluster Method 513

9.3 Brinkman-Rice Transition 520

Solutions to the Problems 525

10 The Correlated Metallic State 527

10.1 The Reduced Fermi Step 527

10.2 Heavy Fermions:Half-Filled Band 530

The Effect of a Strong Magnetic Field 535

Probems 10.1-2 537

10.3 Arbitrary Band Filling 537

Problems 10.3-10.4 542

10.4 The Fermi Volume 542

10.5 The La1-xSrxTiO3 System 543

10.6 Discussion and Outlook 548

10.6.1 Gutzwiller Method:Exact Treatment 549

10.6.2 Metallic and Insulating States 553

Problem 10.5 556

10.6.3 Digression:The l/r Hubbard Chain 556

Problem 10.6 560

10.6.4 Gutzwiller States with Magnetic Order 561

Ferromagnetism 561

Antiferromagnetism 563

Phase Segregation versus Stripe Phases 568

10.6.5 The Infinite-Dimensional Hubbard Model 574

The Correlated Metal 577

Phase Diagram 582

Solutions to the Problems 590

11 Mixed Valence and Heavy Fermions 597

11.1 Lanthanides and Actinides 598

11.2 The Kinds of Valence:Integral,Mixed,Nearly Integral 600

11.2.1 Digression:Valence Skipping 604

11.2.2 Valence Mixing in Rare Earth Compounds 605

11.2.3 Renormalized Hybridized Bands 611

11.2.4 Nearly Integral Valence:Heavy Fermions 619

11.3 Kondo Lattice 628

11.3.1 Kondo Impurity 632

11.3.2 Indirect Exchange 641

11.3.3 Kondo Singlet versus RKKY Magnetism 644

Doniach Phase Diagram 646

Variational Approach 651

Additional Remarks 660

11.4 Rare Earth Magnetism 662

12 Quantum Hall Effect 669

12.1 Introduction 670

12.2 Motion in a Magnetic Field 677

12.2.1 Landau Levels 678

12.2.2 Algebraic Approach 683

12.2.3 Symmetrical Gauge 685

12.3 Integer Quantum Hall Effect 688

12.3.1 High-Field Argument 692

12.3.2 The Gauge Argument 695

12.3.3 Periodic Potential 700

12.4 Fractional Quantum Hall Effect 703

12.4.1 Correlated Many-Electron States 704

Fractionally Charged Quasiparticles 707

Jain States 712

12.5 Discussion and Outlook 715

Phase Diagram 717

Spin Effects 721

A Hydrogen Atom 725

A.1 Hydrogenic Wave Functions 725

A.2 J-Eigenstates 727

B Single-Spin-Flip Ansatz 729

C Gutzwiller Approximation 733

D Schrieffer-Wolff Transformation 741

Bibliography 747

Index 773