J. M. P. Carmelo, J M B Lopes dos Santos, V Rocha Vieira, P D Sacramento, J. M. P. Carmelo, J. M. B. Lopes Dos Santos, V. Rocha Vieira9789812705723, 9812705724
Table of contents :
Preface……Page 8
Strong Correlations, Transport and Dynamics in Complex Materials……Page 12
Contents……Page 14
1.1.1. Introduction……Page 15
1.1.2. Fermi liquid theory……Page 16
1.1.4. Tomonaga and Luttinger models……Page 17
1.1.5. Bosonization……Page 18
1.2. Hubbard model……Page 21
1.2.1. Bethe ansatz solution……Page 22
1.2.2. Landau liquid description……Page 28
1.2.3. Low-temperature thermodynamics……Page 34
1.3. Summary……Page 36
References……Page 37
Contents……Page 40
2.1. Introduction……Page 41
2.2.1. Conductivity: Drude peak and regular part……Page 42
2.2.2. Critical exponents and conformal field theory……Page 45
2.2.3. Finite-energy problems which can be mapped onto a low-energy conformal field theory……Page 51
2.3.1. Pseudoparticles, rotated electrons, and pseudofermions……Page 54
2.3.2. The pseudofermion dynamical theory……Page 59
2.3.3. Application: the one-electron spectral function……Page 62
2.4. Conclusions……Page 67
References……Page 68
Contents……Page 72
3.1. Introduction……Page 73
3.2.1. Undoped compounds……Page 75
3.2.2. Hole doped compounds……Page 76
3.3. Doped-carrier approach of the tt t J model……Page 79
3.3.1. Doped-carrier framework……Page 80
3.3.2. Doped-carrier mean-field theory……Page 81
3.4.1. Mean-field electron operator……Page 84
3.4.2. Mean-field single-electron spectral function……Page 85
3.4.3. Hole doped case……Page 86
3.4.3.1. Dispersive features……Page 87
3.4.3.2. Low energy spectral arcs……Page 89
3.4.3.4. Peak-dip-hump spectral structure……Page 93
3.4.3.5. Spectral weight transfer to low energy: the role of t and t……Page 94
3.4.3.6. Flat dispersion around (0, π) and (π, 0)……Page 95
3.4.3.8. Minimum gap locus topology……Page 96
3.4.3.9. d-wave gap renormalization……Page 97
3.4.4.1. Hole doped versus electron doped……Page 98
3.4.4.2. Electron pockets……Page 100
3.4.4.3. Nodal spectral weight as the signature of superconducting correlations……Page 101
3.4.4.4. d-wave gap renormalization……Page 102
3.5.1. The role of short-range correlations……Page 103
3.5.2. Two-band description of the local energetics……Page 105
3.5.3. Interplay between dSC and AF correlations……Page 107
3.5.4. Doping dependent pseudogap energy……Page 110
3.6. Summary……Page 111
References……Page 112
Contents……Page 122
4.1. Introduction……Page 123
4.1.1. Basic definitions……Page 124
4.2.1. Bulk electronic properties……Page 125
4.2.1.1. The continuum approximation……Page 128
4.2.2. Ribbons of finite width: Surface states……Page 129
4.2.3. Graphene in a perpendicular magnetic field……Page 132
4.2.3.1. Landau levels for the zigzag edge sample……Page 133
4.2.3.2. Landau levels in the continuum approximation……Page 135
4.3. The graphene bilayer……Page 137
4.3.1. Unbiased bilayer (bulk)……Page 138
4.3.1.1. The continuum approximation for the bilayer Hamiltonian……Page 140
4.3.1.2. Landau levels in the continuum approximation for the bilayer……Page 141
4.3.2. Biased bilayer (bulk)……Page 142
4.3.3. Surface states for the bilayer with zigzag edges……Page 146
Acknowledgments……Page 152
References……Page 153
Contents……Page 156
5.1. Introduction……Page 157
5.2. Scattering from impurities……Page 158
5.2.1. Side-jump……Page 159
5.3. Spin chirality and the topological Hall effect……Page 160
5.4. Complex energy spectrum and Berry phase in momentum space……Page 163
5.4.1. Self energy……Page 165
5.4.3. Contribution of states below the Fermi energy……Page 166
5.5. Conclusions……Page 169
References……Page 170
Contents……Page 174
6.1. Introduction……Page 175
6.2. Formalism……Page 178
6.3. Spin system coupled to a time-dependent magnetic field……Page 181
6.3.1. The case of one spin……Page 183
6.3.2. The case of many spins……Page 184
6.4. Domain growth……Page 186
6.4.0.1. Free case……Page 187
6.4.0.2. The interacting case……Page 189
6.4.0.3. Scaling analysis at long times……Page 191
6.5. Conclusions……Page 192
References……Page 194
Contents……Page 198
7.1. Introduction……Page 199
7.2. General nonequilibrium formalism……Page 200
7.3. Nonequilibrium dynamical mean-field theory for the Falicov- Kimball model……Page 202
7.4. Gauge invariance and physical observables……Page 207
7.5. Bloch electrons in infinite dimensions……Page 209
7.6. Exact solution……Page 212
7.7. Perturbation theory……Page 215
References……Page 219
Strongly Correlated Magnetic Systems……Page 222
Contents……Page 224
8.1. Introduction……Page 225
8.2.1. General presentation……Page 226
8.2.2. Choice of the target and model spaces……Page 227
8.2.3. Extraction of the effective Hamiltonian and iteration of the procedure……Page 228
8.3.1. Cohesive energies of the regular 1D spin chain and of the 2D square spin lattice……Page 230
8.3.2. Accumulation points, illustration on the dimerized and the frustrated 1D chains……Page 232
8.3.3. The anisotropic square 2D spin lattice……Page 235
8.3.4. The frustrated 2D Shastry-Sutherland lattice……Page 238
8.4. Conclusion……Page 241
References……Page 242
9.1. Introduction……Page 246
9.2. Edwards-Anderson Model and Spin Glass Order Parameters……Page 248
9.3.1. The SK Model……Page 251
9.3.2. Replica-Symmetric Ansatz……Page 252
9.3.3. Replica Symmetry Breaking: Parisi’s Ansatz……Page 253
9.4. Short-RangeModels……Page 255
9.4.1. The “Droplet” Model……Page 256
9.4.2. Beyond Mean Field Theory……Page 259
9.4.3. Critical Behavior……Page 260
9.5. Conclusion……Page 265
References……Page 266
Contents……Page 270
10.1. Introduction……Page 271
10.2. The double exchange model……Page 273
10.3. The Heisenberg model……Page 275
10.4.1. Confrontation of the model spectra with the ab initio spectrum……Page 276
10.4.2. Confrontation of the model ground state wave-functions with the ab initio one……Page 278
10.5.1. Theory……Page 280
10.5.2. Confrontation of the truncated Hubbard model spectrum to the exact Hamiltonian one and discussion……Page 281
10.5.3. Possible mapping of the truncated Hubbard model on the simpler double exchange and Heisenberg models……Page 282
10.6. Role of the excited Non-Hund states : A refined double exchange model……Page 285
10.7. Conclusion……Page 287
References……Page 288
Contents……Page 290
11.1. Introduction……Page 291
11.2. The Double Exchange Hamiltonian……Page 293
11.3.1. Localization and Off-diagonal Disorder……Page 297
11.3.2. Summary……Page 301
11.4.1. Introduction……Page 303
11.4.2. Overview of Phenomenology……Page 304
11.4.3.1. Theoretical approaches to EuB6……Page 308
11.4.3.2. The Double Exchange Model for EuB6……Page 310
11.4.3.3. The Double Exchange Model and Eu1-xCaxB6……Page 313
References……Page 315
12. Spin transport in magnetic nanowires with domain walls V.K. Dugaev, M.A.N. Araújo, V. Rocha Vieira, P.D. Sacramento, J. Barna´s and J. Berakdar……Page 322
12.1. Introduction……Page 323
12.2. Model and scattering states……Page 324
12.3. Resistance of a thin domain wall……Page 326
12.4. Spin current……Page 327
12.6. Current-induced spin torque……Page 329
12.6.1. Scattering from a single magnetic moment in a magnetic wire……Page 330
12.6.2. Local torque in the magnetic wire with a thin domain wall……Page 331
12.7. Effect of interaction on the transmission of electrons through a thin domain wall……Page 333
12.7.1. Fixed points……Page 338
12.8. Summary and concluding remarks……Page 340
References……Page 342
Quantum Coherent Systems……Page 344
Contents……Page 346
13.1. Introduction……Page 347
13.2.1. The stellar HBT experiment and the transverse coherence length……Page 350
13.2.2. The quantum description……Page 353
13.3.1. Definitions……Page 357
13.3.2. The influence of the ground state population……Page 359
13.3.3. Correlation functions in the momentum space……Page 360
13.4. General introduction to Bose-Einstein condensation. The He experiment……Page 361
13.4.1. Road map to attain Bose-Einstein condensation in dilute atomic gases……Page 362
13.4.2. The metastable Helium Bose-Einstein condensate……Page 363
13.4.3. The magnetic trap and evaporative cooling……Page 364
13.5.1. Atomic density in thermal equilibrium……Page 368
13.5.2. Definition of the critical temperature of an ideal gas confined in a harmonic trap……Page 372
13.5.3. Second order correlation. The different regimes……Page 374
13.5.4. Integrated signals……Page 377
13.6.0.1. Time evolution of a h.o. wave function in free fall……Page 378
13.6.1. Quantum mechanical flux……Page 380
13.6.2. Intensity-intensity correlation function of a expanded cloud……Page 382
13.7. Brief description of experimental results obtained with the He. experiment……Page 386
References……Page 390
14.1. Introduction to density functional theory……Page 396
14.2. Approximate functionals……Page 399
14.3. Some numerical results……Page 403
14.4. The Thomas-Fermi approximation……Page 405
References……Page 413
15.1. Introduction……Page 416
15.2. Kinetic equation for the condensate……Page 419
15.3. Self-phase modulation……Page 422
15.4. Bogoliubov oscillations……Page 424
15.5. Wakefield excitation……Page 425
15.6. Modulational instability……Page 426
15.7. Purely quantum effects……Page 427
15.8. Conclusions……Page 428
References……Page 429
Contents……Page 432
16.1.1. Van Hove singularities……Page 433
16.2. The gap equation……Page 434
16.2.1. Out-of-plane magnetic field……Page 435
16.2.2. Parallel magnetic field……Page 436
16.3.1. The spectral function……Page 437
16.3.2. The pair propagator……Page 438
16.3.4. Zero-temperature critical field……Page 439
16.3.5. NumericalHc2……Page 441
16.4.1. Supercooling field……Page 442
16.4.4. Superheating field……Page 444
16.4.6. Fulde-Ferrel phase……Page 445
16.5.1. Pairing symmetry……Page 446
16.5.3. Doping effects……Page 447
16.6. Van Hove singularities and high-Tc superconductivity……Page 448
16.7. Conclusion……Page 449
References……Page 450
Contents……Page 454
17.1. Introduction……Page 455
17.2. General formalism……Page 456
17.3. Green functions for d-wave superconductor……Page 458
17.4. Impurity perturbations in d-wave superconductor and group expansions for Green functions……Page 462
17.5. Single-impurity approximations……Page 465
17.5.1. Extended impurity center……Page 469
17.5.2. Magnetic perturbation from non-magnetic impurity……Page 475
17.6. Self-consistent approximation and its validity……Page 481
17.6.1. Ioffe-Regel-Mott criterion and validity of SCTMA solutions……Page 487
17.7.1. Interaction matrices and DOS at nodal points……Page 491
17.7.2. Non-magnetic impurities……Page 493
17.7.3. Magnetic impurities……Page 496
17.8. Conclusions……Page 500
References……Page 501
18.1. Introduction……Page 506
18.2. Quarks……Page 507
18.3. Quark Models Old and New8……Page 508
18.4.1. Building Fock Spaces……Page 520
18.4.2. Salpeter Amplitudes……Page 525
18.4.3. Conclusion……Page 530
References……Page 531
Quantum Entanglement……Page 534
Contents……Page 536
19.2. EPR vs. Bell……Page 537
19.3. Definition and Properties……Page 538
19.4.2. The Matrix Product State Representation……Page 543
19.5. Simulation of Many-Body Quantum Systems……Page 544
19.5.1. Entanglement and the Simulation of 1-D Systems……Page 546
19.5.2. Simulation of 1-D Systems for T = 0……Page 547
19.5.3. Simulations of More General Systems……Page 550
Acknowledgments……Page 552
References……Page 554
Contents……Page 560
20.1. Introduction……Page 561
20.1.1. Enters Entanglement………Page 562
20.2. One- and Low-Dimensional Systems……Page 563
20.3. Infinite-Dimensional Systems……Page 567
20.4. Quantum Computation and Quantum Phase Transitions……Page 568
References……Page 572
Contents……Page 578
21.1. Introduction……Page 579
21.2. Entanglement in High-Temperature Superconductivity……Page 582
21.3. Macroscopic Witnesses of Entanglement……Page 585
21.3.1. Magnetic Susceptibility……Page 586
21.3.2. Internal Energy……Page 589
21.3.3. Entanglement in Systems of Non-Interacting Identical Particles……Page 592
21.4. Thermal Entanglement Generation and Manipulation……Page 596
21.4.1. Entanglement Extraction……Page 597
21.4.2. Entanglement Generation……Page 598
21.5. Summary……Page 600
Acknowledgments……Page 601
References……Page 602
Subject Index……Page 606
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