Introduction to frustrated magnetism: materials, experiments, theory
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| Sprache: | English |
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Berlin [u.a.]
Springer
2011
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| Schriftenreihe: | Springer series in solid-state sciences
164 |
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| Beschreibung: | XXVI, 679 S. graph. Darst. |
| ISBN: | 9783642105890 9783642105883 |
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| 245 | 1 | 0 | |a Introduction to frustrated magnetism |b materials, experiments, theory |c Claudine Lacroix ... eds. |
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| adam_text | IMAGE 1
CONTENTS
PART I BASIC CONCEPTS IN FRUSTRATED MAGNETISM 1 GEOMETRICALLY FRUSTRATED
ANTIFERROMAGNETS: STATISTICAL MECHANICS AND DYNAMICS 3
JOHN T. CHALKER 1.1 INTRODUCTION 3
1.2 MODELS 5
1.3 SOME EXPERIMENTAL FACTS 6
1.4 CLASSICAL GROUND STATE DEGENERACY 8
1.5 ORDER BY DISORDER 10
1.6 GROUND STATE CORRELATIONS 14
1.7 DYNAMICS 17
1.8 FINAL REMARKS 21
REFERENCES 21
2 INTRODUCTION TO QUANTUM SPIN LIQUIDS 23
CLAIRE LHUILLIER AND GREGOIRE MISGUICH 2.1 INTRODUCTION 23
2.2 BASIC BUILDING BLOCKS OF VBC AND RVB PHYSICS: THE VALENCE BONDS 27
2.3 VALENCE-BOND CRYSTALS 29
2.3.1 ZEROTH-ORDER VBC WAVE FUNCTION 30
2.3.2 QUANTUM FLUCTUATIONS IN VBCS 31
2.3.3 VBC EXCITATIONS 32
2.4 RESONATING-VALENCE-BOND SPIN LIQUIDS 33
2.5 VBCS OR RVB SPIN LIQUIDS ON KAGOME AND PYROCHLORE LATTICES? 36
2.6 CONCLUSION 38
REFERENCES 39
IX
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1000032647
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
PART II PROBING FRUSTRATED MAGNETS
3 NEUTRON SCATTERING AND HIGHLY FRUSTRATED MAGNETISM 45 STEVEN T.
BRAMWELL 3.1 INTRODUCTION 45
3.2 WHAT NEUTRON SCATTERING MEASURES 47
3.2.1 SCATTERING TRIANGLE 47
3.2.2 PARTIAL DIFFERENTIAL CROSS SECTION 48
3.2.3 RELATION TO SAMPLE PROPERTIES 49
3.2.4 SCATTERING FROM ATOMIC MAGNETIC MOMENTS 50
3.2.5 ORIENTATION FACTOR AND FORM FACTOR 50
3.2.6 GENERAL EXPRESSION FOR THE NEUTRON SCATTERING 51 3.2.7 REAL
EXPERIMENTS 52
3.2.8 POWDER AVERAGING 52
3.2.9 STATIC APPROXIMATION 52
3.2.10 WAVEVECTOR DEPENDENT MAGNETIC MOMENT AND SUSCEPTIBILITY 53
3.2.11 FULLY ORDERED MAGNET 54
3.2.12 MAGNET WITH FUELL OR PARTIAL DISORDER 55
3.2.13 VALIDITY OF THE STATIC APPROXIMATION 55
3.2.14 GENERALISED SUSCEPTIBILITY 56
3.2.15 NEUTRON SPECTROSCOPY 57
3.3 TYPICAL NEUTRON SCATTERING PATTERNS 58
3.3.1 SCATTERING PLANE 58
3.3.2 FREE ENERGY 58
3.3.3 IDEAL PARAMAGNET 60
3.3.4 CONVENTIONAL MAGNET ABOVE TQ 60
3.3.5 CONVENTIONAL MAGNET BELOW 7C 61
3.3.6 COOPERATIVE PARAMAGNET 62
3.3.7 ABSENT PINCH POINTS 63
3.3.8 DYNAMICAL SIGNATURE OF COOPERATIVE PARAMAGNETISM.... 64 3.4
EXPERIMENTAL RESULTS 65
3.4.1 COOPERATIVE PARAMAGNET STATES 65
3.4.2 ORDERED STATES 70
3.4.3 EXCITED STATES 74
3.5 CONCLUSIONS 76
REFERENCES 77
4 NMR AND /XSR IN HIGHLY FRUSTRATED MAGNETS 79
PIETRO CARRETTA AND AMIT KEREN 4.1 BASIC ASPECTS OF NMR AND/SR
TECHNIQUES 79
4.1.1 LINE SHIFT AND LINE WIDTH 80
4.1.2 NUCLEAR AND MUON SPIN-LATTICE RELAXATION RATEL/TI 83
4.1.3 /SR: THE STATIC CASE 85
4.1.4 TSR: THE DYNAMIC CASE 88
IMAGE 3
CONTENTS XI
4.2 FROM ZERO- TO THREE-DIMENSIONAL FRUSTRATED MAGNETS 91 4.2.1
MOLECULAR MAGNETS 91
4.2.2 ANTIFERROMAGNETS ON A SQUARE LATTICE WITH COMPETING INTERACTIONS:
THE JI -J2 MODEL 92 4.2.3 MAGNETIC FRUSTRATION ON A TRIANGULAR LATTICE
95
4.2.4 /XSR AND NMR IN THE SPIN-1 /2 KAGOME LATTICE ZNCU 3 (OH) 6 CL 2 97
4.2.5 THE PROBLEM OF FI + RELAXATION IN SOME KAGOME LATTICES 98
4.2.6 PERSISTENT DYNAMICS AND LATTICE DISTORTIONS IN THE PYROCHLORE
LATTICE 101
REFERENCES 103
5 OPTICAL TECHNIQUES FOR SYSTEMS WITH COMPETING INTERACTIONS 107
JOACHIM DEISENHOFER AND PETER LEMMENS 5.1 INTRODUCTION 107
5.2 INELASTIC LIGHT-SCATTERING 108
5.3 INELASTIC PHONON LIGHT-SCATTERING 110
5.4 INELASTIC MAGNETIC, QUASIELASTIC, AND ELECTRONIC LIGHT SCATTERING
111
5.5 THE IR EXPERIMENT 115
5.6 SPINS, PHONONS, AND LIGHT 116
5.7 SPIN-PHONON INTERACTION IN CR SPINELS 118
5.8 EXCITON-MAGNON ABSORPTION IN KCUF3 122
REFERENCES 124
PART III FRUSTRATED SYSTEMS
6 THE GEOMETRIES OF TRIANGULAR MAGNETIC LATTICES 131
ROBERT J. CAVA, KATHARINE L. HOLMAN, TYREL MCQUEEN, ERIC J. WELSH, D.
VINCENT WEST, AND ANTHONY J. WILLIAMS 6.1 INTRODUCTION 131
6.2 TWO-DIMENSIONAL STRUCTURES 132
6.2.1 PLANES OF EDGE-SHARING TRIANGLES 132
6.2.2 PLANES OF CORNER-SHARING TRIANGLES 136
6.3 THREE-DIMENSIONAL STRUCTURES 141
6.4 NOTE ON SYNTHESIS OF THE COMPOUNDS 151
6.5 CONCLUSION 151
REFERENCES 152
7 HIGHLY FRUSTRATED MAGNETISM IN SPINELS 155
HIDENORI TAKAGI AND SEIJI NIITAKA 7.1 INTRODUCTION 155
7.2 SPINEL STRUCTURE 156
7.3 BASIC ELECTRONIC CONFIGURATION 157
IMAGE 4
XII CONTENTS
7.4 UNIQUENESS OF THE SPINEL AS A FRUSTRATED MAGNET 157
7.5 MATERIALS OVERVIEW OF SPINELS 159
7.6 FRUSTRATION IN SELECTED SPINELS 161
7.6.1 PYROCHLORE ANTIFERROMAGNETS IN SPINEL OXIDES - B-SITE FRUSTRATION
161
7.6.2 FRUSTRATED SPINS ON SPINEL A SITES 167
7.6.3 FRUSTRATED MAGNETS BASED ON CATION- ORDERED SPINELS: THE
HYPER-KAGOME LATTICEOFNA 4 IR 3 O 8 168
7.6.4 CHARGE FRUSTRATION IN MIXED-VALENT SPINELS 171
7.7 SUMMARY 172
REFERENCES 1 73
8 EXPERIMENTAL STUDIES OF PYROCHLORE ANTIFERROMAGNETS 177 BRUCE D.
GAULIN AND JASON S. GARDNER 8.1 INTRODUCTION 177
8.2 THE CUBIC PYROCHLORES 178
8.3 THE SPIN LIQUID GROUND STATE IN TB 2 TI 2 O7 180
8.4 ORDERED GROUND STATES IN TB 2 TI 2 O 7 185
8.5 STRUCTURAL FLUCTUATIONS IN THE SPIN LIQUID STATE OF TB 2 TI 2 O 7
190 8.6 MAGNETIC ORDER AND FLUCTUATIONS IN TB2SN 2 O7 195
8.6.1 PHASE TRANSITIONS AND FLUCTUATIONS IN GD 2 TI 2 0 7 AND GD 2 SN 2
O 7 198
8.7 CONCLUSIONS 203
REFERENCES 204
9 KAGOME ANTIFERROMAGNETS: MATERIALS VS. SPIN LIQUID BEHAVIORS 207
PHILIPPE MENDELS AND ANDREW S. WILLS 9.1 A SHORT THEORETICAL SURVEY:
WHAT WOULD BE THE IDEAL KAGOME ANTIFERROMAGNET? 208
9.2 THEJAROSITES 210
9.2.1 SYNTHESIS AND THE JAROSITE CRYSTAL STRUCTURE: IDEALIZED AND
DISORDERED 210
9.2.2 FE JAROSITES: S = | KAGOME ANTIFERROMAGNETS 215
9.2.3 CR JAROSITES- S = | KAGOME ANTIFERROMAGNETS 217
9.2.4 CONCLUSION 218
9.3 PYROCHLORE SLABS 218
9.3.1 SYNTHESIS 218
9.3.2 MAGNETIC NETWORK 219
9.3.3 GENERIC PHYSICS 220
9.3.4 NON-MAGNETIC DEFECTS 222
9.3.5 CONCLUDING REMARKS 224
9.4 TOWARDSS = 1/2 IDEAL COMPOUNDS 225
9.4.1 VOLBORTHITE 225
IMAGE 5
CONTENTS XIII
9.4.2 HERBERTSMITHITE: AN END TO THE DROUGHT OF QUANTUM SPIN LIQUIDS
[100] 228
9.5 OTHER COMPOUNDS 233
9.5.1 ORGANIC MATERIALS 233
9.5.2 YO. 5 CAO.5BACO 4 0 7 234
9.5.3 LANGASITES 234
9.6 CONCLUSION 235
REFERENCES 236
PART IV SPECIFIE EFFECTS IN FRUSTRATED MAGNETS
10 MAGNETIZATION PLATEAUS 241
MASASHI TAKIGAWA AND FREDERIC MILA 10.1 INTRODUCTION 241
10.2 MECHANISMS FOR FORMATION OF MAGNETIZATION PLATEAUS 242 10.2.1 SPIN
GAP 243
10.2.2 QUANTIZED PLATEAUS 244
10.2.3 ORDER BY DISORDER 245
10.2.4 SUPERFLUID-INSULATOR TRANSITION 246
10.2.5 QUANTUM PLATEAUS 247
10.2.6 HIGH-ORDER PLATEAUS 249
10.2.7 TRANSITION INTO PLATEAUS 250
10.3 EXPERIMENTAL OBSERVATION OF MAGNETIZATION PLATEAUS 251 10.3.1
CLASSICAL PLATEAUS IN TRIANGULAR AND PYROCHLORE LATTICES 252
10.3.2 SRCU 2 (BO 3 ) 2 AND THE SHASTRY-SUTHERLAND MODEL 255 10.3.3
QUANTUM PLATEAUX AND SPIN SUPERSTRUCTURE IN SRCU 2 (BO3) 2 258
10.3.4 PHASE DIAGRAM OF SRCU 2 (BO 3 ) 2 261
10.3.5 RB 4 : A NEW FAMILY OF SHASTRY-SUTHERLAND SYSTEM 263 10.4
CONCLUSION 264
REFERENCES 264
11 SPIN-LATTICE COUPLING IN FRUSTRATED ANTIFERROMAGNETS 269 OLEG
TCHERNYSHYOV AND GIA-WEI CHERN 11.1 INTRODUCTION 269
11.2 SPIN-DRIVEN JAHN-TELLER EFFECT IN A TETRAHEDRON 270
11.2.1 GENERALIZED COORDINATES AND FORCES 271
11.2.2 FOUR 5 = 1/2 SPINS ON A TETRAHEDRON 273
11.2.3 FOUR CLASSICAL SPINS ON A TETRAHEDRON 275
11.2.4 COLOR NOTATION AND OTHER USEFUL ANALOGIES 276 11.2.5
SPIN-JAHN-TELLER EFFECT ON A TRIANGLE 276
11.3 MODELS WITH LOCAL PHONON MODES 278
11.3.1 HALF-MAGNETIZATION PLATEAU IN ACR 2 O 4 SPINELS 279
IMAGE 6
XIV CONTENTS
11.4 COLLECTIVE SPIN-JAHN-TELLER EFFECT ON THE PYROCHLORE LATTICE 280
11.5 COLLECTIVE JAHN-TELLER EFFECT IN CDCR 2 O 4 282
11.5.1 SPIRAL MAGNETIC ORDER IN CDCR 2 O 4 283
11.5.2 THEORYOF SPIRAL MAGNETIC ORDER 284
11.6 SUMMARY AND OPEN QUESTIONS 289
REFERENCES 290
12 SPINKE 293
MICHEL J.P. GINGRAS 12.1 INTRODUCTION 293
12.2 WATER ICE, PAULING ENTROPY, AND ANDERSON MODEL 294
12.2.1 WATER ICE AND PAULING MODEL 294
12.2.2 CATION ORDERING IN INVERSE SPINELS AND ANTIFERROMAGNETIC
PYROCHLORE ISING MODEL 296 12.3 DISCOVERY OF SPIN ICE 298
12.3.1 RARE-EARTH PYROCHLORE OXIDES: GENERALITIES 298 12.3.2 MICROSCOPIC
HAMILTONIAN: TOWARDS AN EFFECTIVE ISING MODEL 299
12.3.3 DISCOVERY OF SPIN ICE IN HO 2 TI 2 O 7 304
12.3.4 NEAREST-NEIGHBOR FERROMAGNETIC (111) ISING MODEL AND PAULING S
ENTROPY 305
12.3.5 RESIDUAL ENTROPY OF DY 2 TI 2 O 7 AND HO 2 TI 2 O 7 307
12.4 DIPOLAR SPIN-ICE MODEL 309
12.4.1 COMPETING INTERACTIONS IN THE DIPOLAR SPIN-ICE MODEL 309
12.4.2 MEAN-FIELD THEORY 312
12.4.3 LOOP MONTE CARLO SIMULATIONS AND PHASE DIAGRAM OF DIPOLAR SPIN
ICE 316
12.4.4 ORIGINOF ICE RULES IN DIPOLAR SPIN ICE 318
12.5 CURRENT RESEARCH TOPICS IN SPIN ICES AND RELATED MATERIALS 319
12.5.1 MAGNETIC-FIELD EFFECTS 319
12.5.2 DYNAMICAL PROPERTIES AND ROLE OF DISORDER 322
12.5.3 BEYOND THE DIPOLAR SPIN-ICE MODEL 322
12.5.4 METALLIC SPIN ICE 322
12.5.5 ARTIFICIAL SPIN ICE 323
12.5.6 STUFFED SPIN ICE 323
12.5.7 QUANTUM MECHANICS, DYNAMICS, AND ORDER IN SPIN ICES 323
12.5.8 COULOMB PHASE, MONOPOLES AND DIRAC STRINGSIN SPIN ICES 324
12.6 CONCLUSION 325
REFERENCES 326
IMAGE 7
CONTENTS XV
13 SPIN NEMATIC PHASES IN QUANTUM SPIN SYSTEMS 331
KARLO PENE AND ANDREAS M. LAEUCHLI 13.1 INTRODUCTION AND MATERIALS 331
13.2 MULTIPOLAR STATES OF A SINGLE SPIN 333
13.3 COMPETITION BETWEEN DIPOLES AND QUADRUPOLES 336
13.3.1 THE BILINEAR-BIQUADRATIC MODEL 336
13.3.2 ENERGY SPECTRA OF SMALL CLUSTERS 338
13.4 QUADRUPOLAR ORDERING IN S = 1 SYSTEMS 340
13.4.1 VARIATIONAL PHASE DIAGRAM 340
13.4.2 ONE- AND TWO-MAGNON INSTABILITY OF THE FULLY POLARIZED STATE 346
13.4.3 SPIN-WAVE THEORY FOR THE FERROQUADRUPOLAR PHASE 347 13.4.4
NUMERICAL APPROACH 353
13.5 FROM CHAINS TO THE SQUARE LATTICE 355
13.6 NEMATIC ORDERING IN S = L/2SYSTEMS 357
13.7 CONCLUSIONS 359
REFERENCES 360
PART V ADVANCED THEORETICAL METHODS AND CONCEPTS IN FRUSTRATED MAGNETISM
14 SCHWINGER BOSONS APPROACHES TO QUANTUM ANTIFERROMAGNETISM 365
ASSA AUERBACH AND DANIEL P. AROVAS 14.1 S J{N) HEISENBERG MODELS 365
14.2 SCHWINGER REPRESENTATION OF SU(7V) ANTIFERROMAGNETS 366 14.2.1
BIPARTITE ANTIFERROMAGNET 367
14.2.2 NON-BIPARTITE (FRUSTRATED) ANTIFERROMAGNETS 368 14.3 MEAN FIELD
HAMILTONIAN 369
14.3.1 MEAN FIELD EQUATIONS 371
14.4 THE MEAN FIELD ANTIFERROMAGNETIC GROUND STATE 373
14.5 STAGGERED MAGNETIZATION IN THE LAYERED ANTIFERROMAGNET 375
REFERENCES 377
15 VARIATIONAL WAVE FUNCTIONS FOR FRUSTRATED MAGNETIC MODELS 379
FEDERICO BECCA, LUCA CAPRIOTTI, ALBERTO PAROLA, AND SANDRO SORELLA 15.1
INTRODUCTION 379
15.2 SYMMETRIES OF THE WAVE FUNCTION: GENERAL PROPERLIES 382 15.3
SYMMETRIES IN THE TWO-DIMENSIONAL CASE 384
15.3.1 THE MARSHALL-PEIERLS SIGN RULE 386
15.3.2 SPIN CORRELATIONS 387
15.4 CONNECTION WITH THE BOSONIC REPRESENTATION 388
15.5 ANTIFERROMAGNETIC ORDER 390
IMAGE 8
XVI CONTENTS
15.6 NUMERICAL RESULTS 392
15.6.1 ONE-DIMENSIONAL LATTICE 392
15.6.2 TWO-DIMENSIONAL LATTICE 396
15.7 OTHER FRUSTRATED LATTICES 402
15.8 CONCLUSIONS 404
REFERENCES 405
16 QUANTUM SPIN LIQUIDS AND FRACTIONALIZATION 407
GREGOIRE MISGUICH 16.1 INTRODUCTION 407
16.2 WHAT IS A SPIN LIQUID? 409
16.2.1 ABSENCE OF MAGNETIC LONG-RANGE ORDER (DEFINITION 1) 409
16.2.2 ABSENCE OF SPONTANEOUSLY BROKEN SYMMETRY (DEFINITION 2) 409
16.2.3 FRACTIONAL EXCITATIONS (DEFINITION 3) 410
16.2.4 HALF-ODD-INTEGER SPINS AND THE LIEB-SCHULTZ-MATTIS-HASTINGS
THEOREM 415
16.3 MEAN FIELDS AND GAUGE FIELDS 416
16.3.1 FERMIONIC REPRESENTATION OF HEISENBERG MODELS 416 16.3.2 LOCAL
SU(2) GAUGE INVARIANCE 418
16.3.3 MEAN-FIELD (SPIN-LIQUID) STATES 418
16.3.4 GAUGE FLUCTUATIONS 422
16.4 Z 2 SPIN LIQUIDS 427
16.4.1 SHORT-RANGE RVB DESCRIPTION 427
16.4.2 Z 2 GAUGE THEORY, SPINON DECONFINEMENT, AND VISONS 428
16.4.3 EXAMPLES 430
16.4.4 HOW TO DETECT A GAPPED Z 2 LIQUID 431
16.5 GAPLESS (ALGEBRAIC) LIQUIDS 432
16.6 OTHER SPIN LIQUIDS 432
16.7 CONCLUSION 433
REFERENCES 433
17 QUANTUM DIMER MODELS 437
RODERICH MOESSNER AND KUMAR S. RAMAN 17.1 INTRODUCTION 437
17.2 HOW QUANTUM DIMER MODELS ARISE 438
17.2.1 LINK VARIABLES AND HARD CONSTRAINTS 438
17.2.2 THE ORIGINOF CONSTRAINTS 439
17.2.3 TUNABLE CONSTRAINTS 440
17.2.4 ADDING QUANTUM DYNAMICS 441
17.3 THE QUANTUM DIMER MODEL HUBERT SPACE 443
17.3.1 TOPOLOGICAL INVARIANTS 443
17.3.2 TOPOLOGICAL ORDER 445
17.3.3 FRACTIONALISATION 446
IMAGE 9
CONTENTS XVII
17.4 QDM PHASE DIAGRAMS 447
17.4.1 GENERAL STRUCTURE OF PHASE DIAGRAMS 447
17.4.2 Z 2 RVB LIQUID PHASE 449
17.4.3 U(L) RVB LIQUID PHASE 451
17.4.4 DECONFINED CRITICAL POINTS 452
17.4.5 VALENCE BOND CRYSTALS 452
17.4.6 SUMMARY OF PHASE DIAGRAMS 455
17.5 THE ROKHSAR-KIVELSON POINT 456
17.5.1 GROUND-STATE WAVEFUNCTION 456
17.5.2 FRACTIONALISATION AND DECONFINEMENT 457
17.5.3 SPATIAL CORRELATIONS 457
17.5.4 EXCITED STATES 458
17.5.5 A SPECIAL LIQUID POINT OR PART OF A LIQUID PHASE? 459 17.6
RESONONS, PHOTONS, AND PIONS: EXCITATIONS IN THE SINGLE MODE
APPROXIMATION 460
17.7 DUALITIES AND GAUGE THEORIES 462
17.7.1 EMERGENCE OF THE QDM 463
17.7.2 CONTINUUM LIMIT OF THE GAUGE THEORY 464
17.8 HEIGHT REPRESENTATION 465
17.9 NUMERICAL METHODS 470
17.10 DIMER PHASES IN SLJ(2) INVARIANT MODELS 471
17.10.1 OVERLAP EXPANSION 472
17.10.2 DECORATION 473
17.10.3 LARGE-N 474
17.10.4 KLEIN MODELS: SU(2) INVARIANT SPIN LIQUIDS 475 17.11 OUTLOOK 475
17.11.1 HOPPING FERMIONS 476
17.11.2 . .. AND MUCH MORE 476
REFERENCES 477
18 NUMERICAL SIMULATIONS OF FRUSTRATED SYSTEMS 48 1
ANDREAS M. LAEUCHLI 18.1 OVERVIEW OF METHODS 481
18.2 CLASSICAL MONTE CARLO 481
18.3 QUANTUM MONTE CARLO 485
18.3.1 STOCHASTIC SERIES EXPANSION (SSE) 485
18.3.2 GREEN-FUNCTION MONTE CARLO 487
18.4 SERIES EXPANSIONS 488
18.4.1 HIGH-TEMPERATURE SERIES 488
18.4.2 7 = 0 PERTURBATIVE EXPANSIONS FOR GROUND- AND EXCITED-STATE
PROPERTIES 489
18.5 DENSITY-MATRIX RENORMALIZATION GROUP (DMRG) 489 18.5.1 FINITET 490
18.5.2 DYNAMICAL RESPONSE FUNCTIONS 490
18.5.3 DMRG IN TWO AND MORE DIMENSIONS 491
IMAGE 10
XVIII CONTENTS
18.6 EXACT DIAGONALIZATION (ED) 491
18.6.1 BASIS CONSTRUCTION 492
18.6.2 CODING OF BASIS STATES 493
18.6.3 SYMMETRIZED BASIS STATES 494
18.6.4 HAMILTONIAN 496
18.6.5 EIGENSOLVERS 497
18.6.6 IMPLEMENTATION DETAILS AND PERFORMANCE ASPECTS 499 18.6.7
OBSERVABLES 500
18.6.8 DYNAMICAL RESPONSE FUNCTIONS 503
18.6.9 TIME EVOLUTION 504
18.6.10 FINITE TEMPERATURES 505
18.7 MISCELLANEOUS FURTHER METHODS 506
18.7.1 CLASSICAL SPIN DYNAMICS (MOLECULAR DYNAMICS) 506 18.7.2
COUPLED-CLUSTER METHOD 506
18.7.3 DYNAMICAL MEAN-FIELD THEORY (DMFT) 507
18.7.4 CONTRACTOR RENORMALIZATION (CORE) 507
18.7.5 SR-RVB CALCULATIONS 507
18.8 SOURCE CODE AVAILABILITY 508
REFERENCES 509
19 EXACT RESULTS IN FRUSTRATED QUANTUM MAGNETISM 513
SHIN MIYAHARA 19.1 INTRODUCTION 513
19.1.1 DIMER MODEL 514
19.2 EXACT RESULTS IN SPIN-1/2 HEISENBERG MODELS 515
19.2.1 EXACT GROUND STATES IN COUPLED TRIANGULAR CLUSTER MODELS 516
19.2.2 EXACT GROUND STATES IN COUPLED TETRAHEDRAL CLUSTER MODELS 522
19.2.3 REALIZATION OF EXACT GROUND STATES 524
19.3 EXACT RESULTS IN FRUSTRATED SPIN-1/2 MODELS WITH FOUR-SPIN
INTERACTIONS 526
19.3.1 GENERAL LADDER MODEL WITH FOUR-SPIN INTERACTIONS 526 19.3.2
TWO-DIMENSIONAL MODEL WITH FOUR-SPIN INTERACTIONS...531 19.4 CONCLUSION
534
REFERENCES 535
20 STRONG-COUPLING EXPANSION AND EFFECTIVE HAMILTONIANS 537 FREDERIC
MILA AND KAI PHILLIP SCHMIDT 20.1 INTRODUCTION 537
20.2 STRONG-COUPLING EXPANSION 538
20.2.1 SECOND-ORDER PERTURBATION THEORY 539
20.2.2 HIGH-ORDER PERTURBATION THEORY 539
20.2.3 EXAMPLES 540
IMAGE 11
CONTENTS XIX
20.3 ALTERNATIVE APPROACHES YIELDING EFFECTIVE HAMILTONIANS 547 20.3.1
CANONICAL TRANSFORMATION 547
20.3.2 CONTINUOUS UNITARY TRANSFORMATION 548
20.3.3 CONTRACTOR RENORMALIZATION 555
20.4 CONCLUSIONS 556
REFERENCES 558
PART VI FRUSTRATION, CHARGE CARRIERS AND ORBITAL DEGENERACY
21 MOBILE HOLES IN FRUSTRATED QUANTUM MAGNETS AND ITINERANT FERMIONS ON
FRUSTRATED GEOMETRIES 563
DIDIER POILBLANC AND HIROKAZU TSUNETSUGU 21.1 INTRODUCTION 563
21.2 DOPING HOLES IN FRUSTRATED QUANTUM MAGNETS 564
21.2.1 THE HOLON-SPINON DECONFINEMENT SCENARIO 564 21.2.2 SINGLE HOLE
DOPED IN FRUSTRATED MOTT INSULATORS 565 21.2.3 HOLE PAIRING AND
SUPERCONDUCTIVITY 568
21.3 DOPED QUANTUM DIMER MODEL 569
21.3.1 ORIGIN OF THE QUANTUM DIMER MODEL 569
21.3.2 PHASE DIAGRAMS AT ZERO DOPING 571
21.3.3 CONNECTION TO THE XXZ MAGNET ON THE CHECKERBOARD LATTICE 571
21.3.4 BOSONIC DOPED QUANTUM DIMER MODEL 573
21.3.5 NON-FROBENIUS DOPED QUANTUM DIMER MODEL ON THE SQUARE LATTICE 574
21.4 MOTT TRANSITION ON THE TRIANGULAER LATTICE 575
21.4.1 FRUSTRATION IN ITINERANT ELECTRON SYSTEMS 575
21.4.2 MOTT TRANSITION IN ORGANIC COMPOUNDS WITH TRIANGULAR GEOMETRY 575
21.4.3 MOTT TRANSITION IN THE TRIANGULAR-LATTICE HUBBARD MODEL 576
21.5 ORDERING PHENOMENA AT COMMENSURATE FERMION DENSITIES ON FRUSTRATED
GEOMETRIES 579
21.5.1 BOND ORDER WAVES FROM NESTING PROPERTIES OF THE FERMI SURFACE 580
21.5.2 METAL-INSULATOR TRANSITIONS AND FRUSTRATED CHARGE ORDER 581
21.5.3 AWAY FROM COMMENSURABILITY: DOPING THE RESONATING-SINGLET-PAIR
CRYSTAL 583
21.6 SUMMARY 584
REFERENCES 584
IMAGE 12
XX CONTENTS
22 METALLIC AND SUPERCONDUCTING MATERIALS WITH FRUSTRATED LATTICES 587
ZENJI HIROI AND MASAO OGATA 22.1 INTRODUCTION 587
22.2 MATERIALS OVERVIEW 590
22.2.1 PYROCHLORE LATTICE 590
22.2.2 TRIANGULAR AND KAGOME LATTICES 596
22.2.3 ORGANIC CONDUCTORS WITH TRIANGULAR LATTICE 599 22.3 THEORETICAL
BACKGROUND 604
22.3.1 RVB SPIN STATE AND RVB SUPERCONDUCTIVITY 604 22.3.2
TRIANGULAR-LATTICE HUBBARD MODEL 607
22.3.3 EXTENDED HUBBARD MODEL FOR ORGANIC CONDUCTORS 609 22.4
SUPERCONDUCTING COMPOUNDS 611
22.4.1 PYROCHLORE LATTICE: CD 2 RE 2 O 7 AND AOS 2 O 6 611
22.4.2 TRIANGULAR LATTICE: NA X COO 2 AND ITS HYDRATE 616 22.4.3
ANISOTROPIE TRIANGULAR LATTICE: ORGANIC SUPERCONDUCTIVITY 620
22.5 SUMMARY 621
REFERENCES 621
23 FRUSTRATION IN SYSTEMS WITH ORBITAL DEGREES OF FREEDOM 629 JEROEN VAN
DEN BRINK, ZOHAR NUSSINOV, AND ANDRZEJ M. OLES 23.1 INTRODUCTION 629
23.2 ORBITAL DEGREES OF FREEDOM 630
23.2.1 ORBITALS AND THEIR ENERGY SCALES 630
23.2.2 COMPARING ORBITAL AND SPIN DEGREES OF FREEDOM 632 23.3 ORBITAL
INTERACTIONS AND ORBITAL MODELS 634
23.3.1 CRYSTAL-FIELD SPLITTING OF ORBITALS 634
23.3.2 JAHN-TELLER DEFORMATION 634
23.3.3 JAHN-TELLER-MEDIATED ORBITAL-ORBITAL INTERACTIONS 636 23.3.4
SUPEREXCHANGE-MEDIATED ORBITAL-ORBITAL INTERACTIONS 638
23.4 SYMMETRY AND SYMMETRY-BREAKING IN ORBITAL MODELS 638 23.4.1 TYPES
OF SYMMETRY IN ORBITAL MODELS 638
23.4.2 EXAMPLES OF INTERMEDIATE SYMMETRIES IN ORBITAL SYSTEMS 639
23.4.3 A THEOREM ON DIMENSIONAL REDUCTION 642
23.4.4 CONSEQUENCES OF THE THEOREM FOR ORBITAL (AND SPIN) ORDERS AND
EXCITATIONS 645
23.5 ORDER BY DISORDER IN CLASSICAL ORBITAL MODELS 646
23.6 CONNECTION WITH QUANTUM COMPUTATION 649
23.6.1 KITAEV S HONEYCOMB MODEL 649
23.6.2 KITAEV S TORIC CODE MODEL 651
23.6.3 RECENT DISCUSSIONS OF QUANTUM COMPUTING REALIZATIONS 652
IMAGE 13
CONTENTS XXI
23.7 SPIN-ORBITAL FRUSTRATION 652
23.7.1 GENERAL STRUCTURE OF SPIN-ORBITAL SUPEREXCHANGE MODELS 652
23.7.2 SPIN-ORBITAL MODELS FOR E G PEROVSKITES 653
23.7.3 SPIN-ORBITAL SUPEREXCHANGE FOR T 2G PEROVSKITES 657 23.7.4
SPIN-ORBITAL FRUSTRATION ON A TRIANGULAR LATTICE 661 23.7.5 SPIN-ORBITAL
FRUSTRATION IN SPINELS 664
23.8 SPIN-ORBITAL ENTANGLEMENT 665
REFERENCES 668
INDEX 671
|
| any_adam_object | 1 |
| author2 | Lacroix, Claudine |
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| dewey-ones | 538 - Magnetism |
| dewey-raw | 538.3 |
| dewey-search | 538.3 |
| dewey-sort | 3538.3 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
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| id | DE-604.BV037233271 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:54:03Z |
| institution | BVB |
| isbn | 9783642105890 9783642105883 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021146893 |
| oclc_num | 707095357 |
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| physical | XXVI, 679 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in solid-state sciences |
| series2 | Springer series in solid-state sciences |
| spelling | Introduction to frustrated magnetism materials, experiments, theory Claudine Lacroix ... eds. Berlin [u.a.] Springer 2011 XXVI, 679 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in solid-state sciences 164 Magnetismus (DE-588)4037021-5 gnd rswk-swf Geometrische Frustration (DE-588)7733821-2 gnd rswk-swf Magnetismus (DE-588)4037021-5 s Geometrische Frustration (DE-588)7733821-2 s DE-604 Lacroix, Claudine edt Springer series in solid-state sciences 164 (DE-604)BV000016582 164 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021146893&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Introduction to frustrated magnetism materials, experiments, theory Springer series in solid-state sciences Magnetismus (DE-588)4037021-5 gnd Geometrische Frustration (DE-588)7733821-2 gnd |
| subject_GND | (DE-588)4037021-5 (DE-588)7733821-2 |
| title | Introduction to frustrated magnetism materials, experiments, theory |
| title_auth | Introduction to frustrated magnetism materials, experiments, theory |
| title_exact_search | Introduction to frustrated magnetism materials, experiments, theory |
| title_full | Introduction to frustrated magnetism materials, experiments, theory Claudine Lacroix ... eds. |
| title_fullStr | Introduction to frustrated magnetism materials, experiments, theory Claudine Lacroix ... eds. |
| title_full_unstemmed | Introduction to frustrated magnetism materials, experiments, theory Claudine Lacroix ... eds. |
| title_short | Introduction to frustrated magnetism |
| title_sort | introduction to frustrated magnetism materials experiments theory |
| title_sub | materials, experiments, theory |
| topic | Magnetismus (DE-588)4037021-5 gnd Geometrische Frustration (DE-588)7733821-2 gnd |
| topic_facet | Magnetismus Geometrische Frustration |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021146893&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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