Field theories of condensed matter physics:
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2013
|
| Edition: | Second edition |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBA01 UBM01 UER01 Volltext Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | 1 Online-Ressource (XVI, 838 Seiten) Diagramme |
| ISBN: | 9781139015509 |
| DOI: | 10.1017/CBO9781139015509 |
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Record in the Search Index
| _version_ | 1804175369528410112 |
|---|---|
| adam_text | Titel: Field theories of condensed matter physics
Autor: Fradkin, Eduardo
Jahr: 2013
Contents
Preface to the second edition page xi
Preface to thefirst edition xv
1 Introduction 1
1.1 Field theory and Condensed matter physics 1
1.2 What has been included in this book (first edition) 2
1.3 What was left out of the first edition 3
1.4 What has been included in the second edition 4
2 The Hubbard model 8
2.1 Introduction 8
2.2 Symmetries of the Hubbard model 10
2.3 The strong-coupling limit 14
2.4 The weak-coupling limit 17
2.5 Correlaüon functions 21
3 The magnetic instability of the Fermi system 27
3.1 Mean-field theory 27
3.2 Path-integral representation of the Hubbard model 39
3.3 Path integrals and mean-field theory 46
3.4 Fluctuations: the non-linear sigma model 51
3.5 The Neel State and the non-linear sigma model 57
4 The renormalization group and scaling 63
4.1 Scale invariance 63
4.2 Examples of fixed points 67
4.3 Scaling behavior of physical observables 72
4.4 General consequences of scale invariance 75
4.5 Perturbative renormalization group about a fixed point 78
4.6 The Kosterlitz renormalization group 82
vi Contents
5 One-dimensional quantum antiferromagnets 90
5.1 The spin-1/2 Heisenberg chain 90
5.2 Fermions and the Heisenberg model 100
5.3 The quantum Ising chain 112
5.4 Duality 116
5.5 The quantum Ising chain as a free-Majorana-fermion System 118
5.6 Abelian bosonization 126
5.7 Phase diagrams and scaling behavior 141
6 The Luttinger liquid 145
6.1 One-dimensional Fermi Systems 145
6.2 Dirac fermions and the Luttinger model 149
6.3 Order parameters of the one-dimensional electron gas 153
6.4 The Luttinger model: bosonization 155
6.5 Spin and the Luttinger model 159
6.6 Scaling and renormalization in the Luttinger model 164
6.7 Correlation functions of the Luttinger model 169
6.8 Susceptibilities of the Luttinger model 176
7 Sigma modeis and topological terms 189
7.1 Generalized spin chains: the Haidane conjecture 189
7.2 Path integrals for spin Systems: the single-spin problem 190
7.3 The path integral for many-spin Systems 198
7.4 Quantum ferromagnets 199
7.5 The effective action for one-dimensional quantum
antiferromagnets 202
7.6 The role of topology 205
7.7 Quantum fluctuations and the renormalization group 209
7.8 Asymptotic freedom and Haldane s conjecture 213
7.9 Hopf term or no Hopf term ? 218
7.10 The Wess-Zumino-Witten model 227
7.11 A (brief) introduction to conformal field theory 233
7.12 The Wess-Zumino-Witten conformal field theory 23 8
7.13 Applications of non-abelian bosonization 243
8 Spin-liquid states 251
8.1 Frustration and disordered spin states 251
8.2 Valence bonds and disordered spin states 253
8.3 Spinons, holons, and valence-bond states 261
8.4 The gauge-field picture of the disordered spin states 263
8.5 Flux phases, valence-bond crystals, and spin liquids 270
Contents vii
8.6 Is the large-N mean-field theory reliable? 277
8.7 SU(2) gauge invariance and Heisenberg modeis 279
9 Gauge theory, dimer modeis, and topological phases 286
9.1 Fluctuations of valence bonds: quantum-dimer modeis 286
9.2 Bipartite lattices: valence-bond order and quantum criticality 290
9.3 Non-bipartite lattices: topological phases 291
9.4 Generalized quantum-dimer modeis 292
9.5 Quantum dimers and gauge theories 294
9.6 The Ising gauge theory 298
9.7 The Z2 confming phase 301
9.8 The Ising deconfming phase: the Z2 topological fluid 305
9.9 Boundary conditions and topology 309
9.10 Generalized 2,2 gauge theory: matter fields 314
9.11 Compact quantum electrodynamics 319
9.12 Deconfmement and topological phases in the U(l) gauge theory 321
9.13 Duality transformation and dimer modeis 325
9.14 Quantum-dimer modeis and monopole gases 336
9.15 The quantum Lifshitz model 342
10 Chiral spin states and anyons 359
10.1 Chiral spin liquids 359
10.2 Mean-field theory of chiral spin liquids 366
10.3 Fluctuations and flux phases 371
10.4 Chiral spin liquids and Chern-Simons gauge theory 375
10.5 The statistics of spinons 382
10.6 Fractional statistics 389
10.7 Chern-Simons gauge theory: a field theory of anyons 393
10.8 Periodicity and families of Chern-Simons theories 398
10.9 Quantization of the global degrees of freedom 400
10.10 Flux phases and the fractional quantum Hall effect 402
10.11 Anyons at finite density 405
10.12 The Jordan-Wigner transformation in two dimensions 412
11 Anyon superconductivity 414
11.1 Anyon superconductivity 414
11.2 The functional-integral formulation of the
Chern-Simons theory 415
11.3 Correl ation functions 417
11.4 The semi-classical approximation 418
11.5 Effective action and topological invariance 424
viii Contents
12 Topology and the quantum Hall effect 432
12.1 Quantum mechanics of charged particles in magnetic fields 432
12.2 The Hofstadter wave functions 438
12.3 The quantum Hall effect 445
12.4 The quantum Hall effect and disorder 447
12.5 Linear-response theory and correlation functions 449
12.6 The Hall conductance and topological invariance 456
12.7 Quantized Hall conductance of a non-interacting system 468
12.8 Quantized Hall conductance of Hofstadter bands 472
13 The fractional quantum Hall effect 480
13.1 The Laughlin wave function 480
13.2 Composite particles 499
13.3 Landau-Ginzburg theory of the fractional quantum Hall effect 502
13.4 Fermion field theory of the fractional quantum Hall effect 512
13.5 The semi-classical excitation spectrum 523
13.6 The electromagnetic response and collective modes 525
13.7 The Hall conductance and Chern-Simons theory 528
13.8 Quantum numbers of the quasiparticles: fractional Charge 530
13.9 Quantum numbers of the quasiparticles: fractional statistics 534
14 Topological fluids 536
14.1 Quantum Hall fluids on a torus 536
14.2 Hydrodynamic theory 542
14.3 Hierarchical states 547
14.4 Multi-component abelian fluids 552
14.5 Superconductors as topological fluids 556
14.6 Non-abelian quantum Hall states 563
14.7 The spin-singlet Halperin states 573
14.8 Moore-Read states and their generalizations 575
14.9 Topological superconductors 587
14.10 Braiding and fusion 597
15 Physics at the edge 603
15.1 Edge states of integer quantum Hall fluids 603
15.2 Hydrodynamic theory of the edge states 609
15.3 Edges of general abelian quantum Hall states 620
15.4 The bulk-edge correspondence 624
15.5 Effective-field theory of non-abelian states 641
15.6 Tunneling conductance at point contacts 647
15.7 Noise and fractional charge 661
Contents ix
15.8 Quantum interferometers 662
15.9 Topological quantum computation 667
16 Topological insulators 669
16.1 Topological insulators and topological band structures 669
16.2 The integer quantum Hall effect as a topological insulator 670
16.3 The quantum anomalous Hall effect 672
16.4 The quantum spin Hall effect 687
16.5 Z2 topological invariants 696
16.6 Three-dimensional topological insulators 701
16.7 Solitons in polyacetylene 705
16.8 Edge states in the quantum anomalous Hall effect 714
16.9 Edge states and the quantum spin Hall effect 718
16.10 Z2 topological insulators and the parity anomaly 720
16.11 Topological insulators and interactions 733
16.12 Topological Mott insulators and nematic phases 736
16.13 Topological insulators and topological phases 745
17 Quantum entanglement 753
17.1 Classical and quantum criticality 753
17.2 Quantum entanglement 756
17.3 Entanglement in quantum field theory 758
17.4 Thearealaw 762
17.5 Entanglement entropy in conformal field theory 765
17.6 Entanglement entropy in the quantum Lifshitz universality class 769
17.7 Entanglement entropy in cpA theory 778
17.8 Entanglement entropy and holography 780
17.9 Quantum entanglement and topological phases 785
17.10 Outlook 795
References 799
Index 826
|
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| discipline | Physik |
| doi_str_mv | 10.1017/CBO9781139015509 |
| edition | Second edition |
| format | Electronic eBook |
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| spelling | Fradkin, Eduardo 1950- Verfasser (DE-588)1033021873 aut Field theories of condensed matter physics Eduardo Fradkin, University of Illinois at Urbana-Champaign Second edition Cambridge Cambridge University Press 2013 1 Online-Ressource (XVI, 838 Seiten) Diagramme txt rdacontent c rdamedia cr rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 gnd rswk-swf Kondensierte Materie (DE-588)4132810-3 s Quantenfeldtheorie (DE-588)4047984-5 s DE-604 https://doi.org/10.1017/CBO9781139015509 Verlag URL des Erstveröffentlichers Volltext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028443734&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fradkin, Eduardo 1950- Field theories of condensed matter physics Quantenfeldtheorie (DE-588)4047984-5 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4132810-3 |
| title | Field theories of condensed matter physics |
| title_auth | Field theories of condensed matter physics |
| title_exact_search | Field theories of condensed matter physics |
| title_full | Field theories of condensed matter physics Eduardo Fradkin, University of Illinois at Urbana-Champaign |
| title_fullStr | Field theories of condensed matter physics Eduardo Fradkin, University of Illinois at Urbana-Champaign |
| title_full_unstemmed | Field theories of condensed matter physics Eduardo Fradkin, University of Illinois at Urbana-Champaign |
| title_short | Field theories of condensed matter physics |
| title_sort | field theories of condensed matter physics |
| topic | Quantenfeldtheorie (DE-588)4047984-5 gnd Kondensierte Materie (DE-588)4132810-3 gnd |
| topic_facet | Quantenfeldtheorie Kondensierte Materie |
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