Verfügbarkeit: Topological aspects of condensed matter physics

Topological aspects of condensed matter physics: École de physique des Houches, Session CIII, 4-29 August 2014

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Bibliographische Detailangaben
Körperschaft:	École de physique des Houches Les Houches (VerfasserIn)
Weitere beteiligte Personen:	Chamon, Claudio (HerausgeberIn), Goerbig, Mark Oliver (HerausgeberIn), Moessner, Roderich (HerausgeberIn), Cugliandolo, Leticia F. 1965- (HerausgeberIn)
Format:	Tagungsbericht Buch
Sprache:	Englisch
Veröffentlicht:	Oxford Oxford University Press 2017
Ausgabe:	First edition
Schriftenreihe:	Session 103
Schlagwörter:	Quantentheorie Mathematische Physik Topologie Kondensierte Materie Condensed matter Quantum theory Konferenzschrift > 04.08.2014-29.08.2014 > Les Houches
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029950116&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Includes bibliographical references
Umfang:	xxxi, 671 Seiten Illustrationen 26 cm
ISBN:	9780198785781

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adam_text	Contents List of Participants xxvii Part I Basic Lectures 1 An introduction to topological phases of electrons 3 Joel E. MOORE 1.1 Introduction 5 1.2 Basic concepts 5 1.2.1 Mathematical preliminaries 5 1.2.2 Berry phases in quantum mechanics 14 1.3 Topological phases: Thouless phases arising from Berry phases 18 1.3.1 Bloch states 18 1.3.2 ID polarization and 2D IQHE 21 1.3.3 Interactions and disorder; the flux trick 23 1.3.4 TKNN integers, Chern numbers, and homotopy 24 1.3.5 Time-reversal invariance in Fermi systems 26 1.3.6 Experimental status of 2D insulating systems 29 1.3.7 3D band structure invariants and topological insulators 29 1.3.8 Axion electrodynamics, second Chern number, and magnetoelectric polarizability 31 1.3.9 Anomalous Hall effect and Karplus—Luttinger anomalous velocity 35 1.4 Introduction to topological order 35 1.4.1 FQHE background 35 1.4.2 Topological terms in field theories: the Haldane gap and Wess-Zumino-Witten models 36 1.4.3 Topologically ordered phases: the FQHE 45 l.A Topological invariants in 2D with time-reversal invariance 55 l.A.l An interlude: Wess—Zumino terms in ID nonlinear T-models 55 l.A.2 Topological invariants in time-reversal-invariant Fermi systems 56 1.A.3 Pumping interpretation of Z2 invariant 58 References 59 2 Topological superconductors and category theory 63 Andrei BERNEVIG and Titus NEUPERT Preface 65 2.1 Introduction to topological phases in condensed matter 65 2.1.1 The notion of topology 65 2.1.2 Classification of non-interacting fermion Hamiltonians: the 10-fold way 67 xviii Contents 2.1.3 The Su-Schrieffer-Heeger model 75 2.1.4 The ID p-wave superconductor 77 2.1.5 Reduction of the 10֊fold way classification by interactions: Z ---► Zg in class BDI 80 2.2 Examples of topological order 82 2.2.1 The toric code 83 2.2.2 The 2D p-wave superconductor 90 2.3 Category theory 102 2.3.1 Fusion category 102 2.3.2 Braiding category 110 2.3.3 Modular matrices 114 2.3.4 Examples: the 16-fold way revisited 118 Acknowledgements 120 References 121 Spin liquids and frustrated magnetism 123 John T. CHALKER 3.1 Introduction 125 3.1.1 Overview 125 3.1.2 Classical ground-state degeneracy 128 3.1.3 Order by disorder 129 3.2 Classical spin liquids 132 3.2.1 Simple approximations 132 3.2.2 The triangular lattice Ising antiferromagnet and height models 134 3.3 Classical dimer models 137 3.3.1 Introduction 138 3.3.2 General formulation 138 3.3.3 Flux sectors, and i7(l) and Z2 theories 141 3.3.4 Excitations 142 3.4 Spin ices 143 3.4.1 Materials 143 3.4.2 Coulomb phase correlations 144 3.4.3 Monopoles 147 3.4.4 Dipolar interactions 148 3.5 Quantum spin liquids 150 3.5.1 Introduction 150 3.5.2 Lieb-Schultz-Mattis theorem 150 3.5.3 Quantum dimer models 152 3.6 Concluding remarks 160 3.6.1 Slave particles 160 3.6.2 Numerics 161 3.6.3 Summary 161 Acknowledgements 162 References 162 Contents хіх 4 Entanglement spectroscopy and its application to the quantum Hall effects 165 Nicolas REGNAULT Preface 167 4.1 Introduction 167 4.2 Entanglement spectrum and entanglement entropy 169 4.2.1 Definitions 170 4.2.2 A simple example: two spin-·^ 171 4.2.3 Entanglement entropy 172 4.2.4 The AKLT spin chain 175 4.2.5 Matrix product states and the entanglement spectrum 177 4.3 Observing an edge mode through the entanglement spectrum 179 4.3.1 The integer quantum Hall effect 179 4.3.2 Chern insulators 184 4.3.3 Entanglement spectrum for a Cl 185 4.4 Fractional quantum Hall effect and entanglement spectra 189 4.4.1 Fractional quantum Hall effect: overview and notation 190 4.4.2 Orbital entanglement spectrum 193 4.4.3 OES beyond model wavefunctions 197 4.4.4 Particle entanglement spectrum 201 4.4.5 Real-space entanglement spectrum 204 4.5 Entanglement spectrum as a tool: probing the fractional Chern insulators 205 4.5.1 From Chern insulators to fractional Chern insulators 205 4.5.2 Entanglement spectrum for fractional Chern insulators 208 4.6 Conclusions 209 Acknowledgements 210 References 210 Part II Topical lectures 5 Duality in generalized Ising models 219 Franz J. WEGNER Preface 221 5.1 Introduction 221 5.2 Kramers-Wannier duality 221 5.2.1 High-temperature expansion (HTE) 222 5.2.2 Low-temperature expansion (LTE) 223 5.2.3 Comparison 223 5.3 Duality in three dimensions 224 5.4 General Ising models and duality 223 5.4.1 General Ising models 223 5.4.2 Duality 223 5.5 Lattices and Ising models 229 5.5.1 Lattices and their dual lattices 229 xx Contents 5.5.2 Models on the lattice 230 5.5.3 Euler characteristic and degeneracy 230 5.6 The models on hypercubic lattices 232 5.6.1 Gauge invariance and degeneracy 233 5.6.2 Self-duality 233 5.7 Correlations 234 5.7.1 The model Mdd 234 5.7.2 Dislocations 235 5.8 Lattice gauge theories 237 5.9 Electromagnetic field 237 References 238 6 Topological insulators and related phases with strong interactions 241 Ashvin VISHWANATH 6.1 Overview 243 6.2 Quantum phases of matter. Short-range versus long-range entanglement 244 6.3 Examples of SRE topological phases 247 6.3.1 Haldane phase of S ~ 1 antiferromagnet in d = 1 247 6.3.2 An exactly soluble topological phase in d = 1 247 6.4 SRE phase of bosons in two dimensions 249 6.4.1 Coupled-wire construction 250 6.4.2 Effective field theory 252 6.4.3 Implications for IQH state of electrons 254 6.5 SPT phases of bosons in three dimensions 255 6.5.1 The m = 0 critical point 257 6.5.2 Surface topological order of 3D bosonic SRE phases 257 6.6 Surface topological order of fermionic topological insulators and superconductors 260 Acknowledgements 262 References 262 7 Fractional Abelian topological phases of matter for fermions in two-dimensional space 265 Christopher MUDRY 7.1 Introduction 268 7.2 The tenfold way in quasi-one-dimensional space 277 7.2.1 Symmetries for the case of one one-dimensional channel 277 7.2.2 Symmetries for the case of two one-dimensional channels 283 7.2.3 Definition of the minimum rank 286 7.2.4 Topological spaces for the normalized Dirac masses 289 7.3 Fractionalization from Abelian bosonization 289 7.3.1 Introduction 289 7.3.2 Definition 290 Contents xxi 7.3.3 Chiral equations of motion 291 7.3.4 Gauge invariance 292 7.3.5 Conserved topological charges 295 7.3.6 Quasiparticle and particle excitations 297 7.3.7 Bosonization rules 300 7.3.8 From the Hamiltonian to the Lagrangian formalism 303 7.3.9 Applications to polyacetylene 305 7.4 Stability analysis for the edge theory in symmetry class AII 307 7.4.1 Introduction 307 7.4.2 Definitions 312 7.4.3 Time-reversal symmetry of the edge theory 314 7.4.4 Pinning the edge fields with disorder potentials: the Haldane criterion 316 7.4.5 Stability criterion for edge modes 317 7.4.6 The stability criterion for edge modes in the FQSHE 320 7.5 Construction of two-dimensional topological phases from coupled wires 322 7.5.1 Introduction 322 7.5.2 Definitions 326 7.5.3 Strategy for constructing topological phases 330 7.5.4 Reproducing the tenfold way 334 7.5.5 Fractionalized phases 344 7.5.6 Summary 350 Acknowledgements 351 References 351 8 Symmetry-protected topological phases in one-dimensional systems 361 Frank POLLMANN 8.1 Introduction 363 8.2 Entanglement and matrix product states 364 8.2.1 Schmidt decomposition and entanglement 364 8.2.2 Area law 366 8.2.3 Matrix product states 367 8.3 Symmetry-protected topological phases 372 8.3.1 Symmetry transformations of MPS 372 8.3.2 Classification of projective representations 374 8.3.3 Symmetry fractionalization 375 8.3.4 Spin-1 chain and the Haldane phase 377 8.4 Detection 378 8.4.1 Degeneracies in the entanglement spectrum 378 8.4.2 Extraction of projective representations from the mixed transfer matrix 379 8.4.3 String order parameters 380 383 383 383 387 389 389 392 394 394 397 398 400 400 400 402 403 405 406 407 408 410 420 423 423 425 427 430 430 435 437 438 441 444 444 446 447 447 451 453 453 453 455 457 xxii Contents 8.5 Summary Acknowledgement References 9 Topological superconducting phases in one dimension Felix von OPPEN, Yang PENG, and Falko PIENTKA 9.1 Introduction 9.1.1 Motivation 9.1.2 Heuristic arguments 9.2 Spinless p-wave superconductors 9.2.1 Continuum model and phase diagram 9.2.2 Domain walls and Major ana excitations 9.2.3 Topological protection and many-body ground states 9.2.4 Experimentally accessible systems 9.3 Topological insulator edges 9.3.1 Model and phases 9.3.2 Zero-energy states and Majorana operators 9.4 Quantum wires 9.4.1 Kitaev limit 9.4.2 Topological insulator limit 9.5 Chains of magnetic adatoms on superconductors 9.5.1 Shiba states 9.5.2 Adatom chains 9.5.3 Kitaev chain 9.6 Non-Abelian statistics 9.6.1 Manipulation of Majorana bound states 9.6.2 Non-Abelian Berry phase 9.6.3 Braiding Majorana zero modes 9.7 Experimental signatures 9.7.1 Conductance signatures 9.7.2 4TT-periodic Josephson effect 9.8 Conclusions 9.A Pairing Hamiltonians: BdG and second quantization 9.B Proximity-induced pairing 9.C Shiba states 9.C.1 Adatom as a classical magnetic impurity 9.C.2 Adatom as a spin-֊ Anderson impurity Acknowledgements References 10 Transport of Dirac surface states D. Carpentier 10.1 Introduction 10.1.1 Purpose of the lectures 10.1.2 Dirac surface states of topological insulators 10.1.3 Graphene 10.1.4 Overview of transport properties Contents xxiii 10.2 Minimal conductivity close to the Dirac point 458 10.2.1 Zitterbewegung 458 10.2.2 Clean large tunnel junction 459 10.2.3 Minimal conductivity from linear response theory 460 10.3 Classical conductivity at high Fermi energy 461 10.3.1 Boltzmann equation 462 10.3.2 Linear response approach 466 10.4 Quantum transport of Dirac fermions 472 10.4.1 Quantum correction to the conductivity: weak antilocalization 474 10.4.2 Universal conductance fluctuations 477 10.4.3 Notion of universality class 479 10.4.4 Effect of a magnetic field 483 Acknowledgements 484 References 484 11 Spin textures in quantum Hall systems 489 Benoît DOUÇOT 11.1 Introduction 491 11.2 Physical properties of spin textures 493 11.2.1 Intuitive picture 493 11.2.2 Construction of spin textures 497 11.2.3 Energetics of spin textures 501 11.2.4 Choice of an effective model 503 11.2.5 Classical ground states of the CPd~l model 507 11.3 Periodic textures 508 11.3.1 Perturbation theory for degenerate Hamiltonians 508 11.3.2 Remarks on the Hessian of the exchange energy 511 11.3.3 Variational procedure for energy minimization 513 11.3.4 Properties of periodic textures 516 11.4 Collective excitations around periodic textures 517 11.4.1 Time-dependent Hartree-Fock equations 517 11.4.2 Collective-mode spectrum 518 11.4.3 Towards an effective sigma model description 521 11.A Coherent states in the lowest Landau level 522 ll.B From covariant symbols on a two-dimensional plane to operators 523 ll.C Single-particle density matrix in a texture Slater determinant 524 ll.D Hamiltonians with quadratic covariant symbol 526 Acknowledgements 527 References 527 12 Out-of-equilibrium behaviour in topologically ordered systems on a lattice: fractionalized excitations and kinematic constraints 531 Claudio CASTELNOVO Preface 533 12.1 Topological order, broadly interpreted 533 xxiv Contents 12.2 Example 1: (classical) spin ice 534 12.2.1 Thermal quenches 538 12.2.2 Field quenches 545 12.3 Example 2: Kitaev’s toric code 552 12.3.1 The model 553 12.3.2 Elementary excitations 555 12.3.3 Dynamics 557 12.3.4 Intriguing comparison: kinetically constrained models 559 12.4 Conclusions 564 Acknowledgements 564 References 565 13 What is life?—70 years after Schrödinger 567 Antti J. NIEMI Preface 570 13.1 A protein minimum 571 13.1.1 Why proteins? 571 13.1.2 Protein chemistry and the genetic code 572 13.1.3 Data banks and experiments 573 13.1.4 Phases of proteins 577 13.1.5 Backbone geometry 580 13.1.6 Ramachandran angles 582 13.1.7 Homology modelling 584 13.1.8 All-atom models 585 13.1.9 All-atom simulations 587 13.1.10 Thermostats 588 13.1.11 Other physics-based approaches 592 13.2 Bol’she 592 13.2.1 The importance of symmetry breaking 593 13.2.2 An optical illusion 593 13.2.3 Fractional charge 594 13.2.4 Spin-charge separation 596 13.2.5 All-atom is Landau liquid 598 13.3 Strings in three space dimensions 599 13.3.1 Abelian Higgs model and the limit of slow spatial variations 600 13.3.2 The Frenet equation 602 13.3.3 Frame rotation and Abelian Higgs multiplet 603 13.3.4 The unique string Hamiltonian 605 13.3.5 Integrable hierarchy 605 13.3.6 Strings from solitons 606 13.3.7 Anomaly in the Frenet frames 608 13.3.8 Perestroika 610 13.4 Discrete Frenet frames 612 13.4.1 The Cct trace reconstruction 614 13.4.2 Universal discretized energy 615 Contents XXV 13.4.3 Discretized solitons 618 13.4.4 Proteins out of thermal equilibrium 619 13.4.5 Temperature renormalization 620 13.5 Solitons and ordered proteins 624 13.5.1 A-repressor as a multisoliton 624 13.5.2 Structure of myoglobin 628 13.5.3 Dynamical myoglobin 635 13.6 Intrinsically disordered proteins 646 13.6.1 Order versus disorder 647 13.6.2 hlAPP and type 2 diabetes 649 13.6.3 hlAPP as a three-soliton 651 13.6.4 Heating and cooling hlAPP 655 13.7 Beyond Ca 659 13.7.1 ‘What-you-see-is-what-you-have5 660 Acknowledgements 666 References 666
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genre_facet	Konferenzschrift 04.08.2014-29.08.2014 Les Houches
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isbn	9780198785781
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-029950116
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owner	DE-355 DE-BY-UBR DE-91G DE-BY-TUM
owner_facet	DE-355 DE-BY-UBR DE-91G DE-BY-TUM
physical	xxxi, 671 Seiten Illustrationen 26 cm
publishDate	2017
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publisher	Oxford University Press
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spellingShingle	Topological aspects of condensed matter physics École de physique des Houches, Session CIII, 4-29 August 2014 Session Quantentheorie Mathematische Physik (DE-588)4037952-8 gnd Topologie (DE-588)4060425-1 gnd Kondensierte Materie (DE-588)4132810-3 gnd
subject_GND	(DE-588)4037952-8 (DE-588)4060425-1 (DE-588)4132810-3 (DE-588)1071861417
title	Topological aspects of condensed matter physics École de physique des Houches, Session CIII, 4-29 August 2014
title_auth	Topological aspects of condensed matter physics École de physique des Houches, Session CIII, 4-29 August 2014
title_exact_search	Topological aspects of condensed matter physics École de physique des Houches, Session CIII, 4-29 August 2014
title_full	Topological aspects of condensed matter physics École de physique des Houches, Session CIII, 4-29 August 2014 edited by Claudio Chamon (Physics Department, Boston University, Boston, Massachusetts, 02215, USA), Mark O. Goerbig (Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, Université Paris-Saclay F-91405, France), Roderich Moessner (Max-Planck-Institut für Physikl komplexer Systeme, 901187 Dresden, Germany), Leticia F. Cugliandolo (Sorbornn Universités, Universités Pierre et Marie Curie, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, Paris, France)
title_fullStr	Topological aspects of condensed matter physics École de physique des Houches, Session CIII, 4-29 August 2014 edited by Claudio Chamon (Physics Department, Boston University, Boston, Massachusetts, 02215, USA), Mark O. Goerbig (Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, Université Paris-Saclay F-91405, France), Roderich Moessner (Max-Planck-Institut für Physikl komplexer Systeme, 901187 Dresden, Germany), Leticia F. Cugliandolo (Sorbornn Universités, Universités Pierre et Marie Curie, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, Paris, France)
title_full_unstemmed	Topological aspects of condensed matter physics École de physique des Houches, Session CIII, 4-29 August 2014 edited by Claudio Chamon (Physics Department, Boston University, Boston, Massachusetts, 02215, USA), Mark O. Goerbig (Laboratoire de Physique des Solides, CNRS UMR 8502, Université Paris-Sud, Université Paris-Saclay F-91405, France), Roderich Moessner (Max-Planck-Institut für Physikl komplexer Systeme, 901187 Dresden, Germany), Leticia F. Cugliandolo (Sorbornn Universités, Universités Pierre et Marie Curie, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, Paris, France)
title_short	Topological aspects of condensed matter physics
title_sort	topological aspects of condensed matter physics ecole de physique des houches session ciii 4 29 august 2014
title_sub	École de physique des Houches, Session CIII, 4-29 August 2014
topic	Quantentheorie Mathematische Physik (DE-588)4037952-8 gnd Topologie (DE-588)4060425-1 gnd Kondensierte Materie (DE-588)4132810-3 gnd
topic_facet	Quantentheorie Mathematische Physik Topologie Kondensierte Materie Konferenzschrift 04.08.2014-29.08.2014 Les Houches
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029950116&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000022608
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