Boulevard Of Broken Symmetries: Effective Field Theories Of Condensed Matter

by Adriaan M J Schakel

Overview

This textbook covers the main topics in contemporary condensed matter physics in a modern and unified way, using quantum field theory in the functional-integral approach. The book highlights symmetry aspects in acknowledging that much of the collective behaviors of condensed matter systems at low temperatures emerge above a nontrivial ground state, which spontaneously breaks the symmetry.The emphasis is on effective field theories which provide an efficient and powerful description that is valid at long wavelengths and low frequencies. In conjunction with the emphasis on effective theories, a modern approach towards renormalization is taken, whereby a wavenumber cut-off is introduced to set a scale beyond which the microscopic model under consideration ceases to be valid.The unique and innovative character of this presentation, free of historical constraints, allows for a compact and self-contained treatment of the main topics in contemporary condensed matter physics.

Product Details

ISBN-13:	9789812813909
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	10/30/2008
Pages:	412
Product dimensions:	6.00(w) x 9.10(h) x 1.10(d)

Table of Contents

Preface vii

Synopsis xi

Notation and Conventions xv

1 Classical Field Theory 1

1.1 One-Dimensional Crystal 1

1.2 Action Principle 2

1.3 Noether's Theorem 3

1.4 Nonrelativistic Field Theory 7

1.5 Spontaneously Broken Symmetries 11

1.6 Effective Theory of Hydrodynamics 14

1.7 Sound Waves 16

1.8 Topological Defects 19

1.9 Homotopy Groups 21

1.10 Quantized Vortices 26

1.11 Villain Vector Potential 27

2 Quantum Field Theory 31

2.1 Quantum Statistical Mechanics 31

2.2 Finite-Temperature Field Theory 36

2.3 Functional Integrals 38

2.4 Feynman Propagator 42

2.5 Feynman Diagrams 47

2.6 Connected Green Functions 53

2.7 Effective Action 55

2.8 Linear Response Theory 59

2.9 Ward Identities 64

3 Calculation Tools 67

3.1 Derivative Expansion 67

3.2 Free Electron Gas in an External Magnetic Field 69

3.3 Goldstone-Wilczek Currents 71

3.4 Optical Phonons 75

3.5 Geometric Phase 77

3.6 Monopole Action 81

3.7 Wess-Zumino Terms 84

3.8 Landau-Levels Technique 86

3.9 Magnetic Susceptibility of an Electron Gas 91

4 Bose-Einstein Condensation 95

4.1 Ideal Bose Gas 95

4.2 Critical Properties 97

4.3 Ideal Bose Gas in a Harmonic Trap 100

4.4 Gross-Pitaevskii Theory 102

4.5 Bogoliubov Theory 104

4.6 Renormalization 106

4.7 One-Loop Corrections 110

4.8 Phonon Decay 114

4.9 Effective Theory 115

4.10 Finite Temperature 120

4.11 Large-N Expansion 128

4.12 Two-Fluid Model 132

4.13 Impurities 136

4.14 Bose-Hubbard Model 138

5 Vortices in 2D 147

5.1 Vortex Dynamics 147

5.2 2D Coulomb Gas 153

5.3 Berezinskii-Kosterlitz-Thouless Transition 155

5.4 Sine-Gordon Model 159

5.5 Superfluid 4He Films 163

5.6 Duality165

6 Fermi Gases 169

6.1 Interacting Fermi Gas 169

6.2 Impurities 172

6.3 Conductivity 175

6.4 Kondo Effect 179

6.5 Degenerate Electron Gas 183

6.6 Thermodynamic Potential 190

6.7 Self-Energy 194

7 Magnetic Order in Fermi Systems 197

7.1 Hubbard Model 197

7.2 Ferromagnetic State 201

7.3 Ferromagnetic Spin Waves 203

7.4 Antiferromagnetic State 207

7.5 Antiferromagnetic Spin Waves 210

8 Superconductivity 213

8.1 BCS Theory 213

8.2 Gap Equation 214

8.3 Anderson-Bogoliubov Mode 218

8.4 Linear Response 221

8.5 Flux Quantization 223

8.6 Plasma Mode 224

8.7 Josephson Effect 225

8.8 Effective Potential 227

8.9 Effective Action 228

8.10 Ginzburg-Landau Theory 229

8.11 Condensation Energy 234

8.12 Ginzburg Region 236

8.13 Magnetic Vortices 238

8.14 Mixed State 243

8.15 Gapless Superconductivity 246

9 Duality 253

9.1 Superconducting Films 253

9.2 Bosonization 259

9.3 Chiral Anomaly 263

9.4 Fermion Condensate 265

9.5 Index Theorem 268

9.6 Vacuum 271

9.7 Massive Schwinger Model 275

9.8 Peierls Instability 277

9.9 Fractional Charge 281

10 From BCS to BEC 285

10.1 Composite Boson Limit 285

10.2 Ultracold Fermi Gases 288

10.3 Derivative Expansion 289

10.4 Quantum Phase Transitions 292

10.5 Superconductor-Insulator Transition 294

11 Superfluid 3He 299

11.1 P-State Triplet Pairing 299

11.2 Phase Diagram 304

11.3 Fermionic Excitations 307

11.4 Boojums 310

11.5 Callan-Harvey Effect 313

11.6 Wess-Zumino Term 318

11.7 Topological Defects 321

12 Quantum Hall Effect 327

12.1 2D Electron Gas in a Strong Magnetic Field 328

12.2 Many-Particle Wave Function 331

12.3 Fluxons 335

12.4 IQHE 338

12.5 Laughlin Wave Function 340

12.6 Composite Fermions 341

12.7 Fractional Charge 343

12.8 Near v = 1/2 344

12.9 Aharonov-Bohm Effect 346

12.10 Chern-Simons Theory 347

12.11 Graphene 350

Bibliography 357

Author Index 373

Index 379