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Bibliografická citace

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BK
First published
Cambridge : Cambridge University Press, 2015
xv, 796 stran : ilustrace (některé barevné) ; 26 cm

objednat
ISBN 978-0-521-86488-6 (vázáno)
Obsahuje bibliografie a rejstříky
Popsáno podle 3. dotisku z roku 2019
001635971
Introduction to Many-Body Physics // “Coleman begins with the basics of quantum mechanics, but manages to engagingly and deftly introduce the reader to the important ideas of many-body physics within a few chapters. [His] expert guidance then helps make a seemingly effortless step to the physics of modern correlated electron compounds. I enthusiastically recommend this book to all graduate students in physics.” // Subir Sachdev, Harvard University // “This book offers the chance to learn from an accomplished expert and, just as important, from an enthusiast for quantum many-body physics. It will be essential reading for graduate students entering the rich universe of quantum many-particle phenomena [and] a chance to learn from a master. The easy-going style, the historical context and, critically, the worked examples and exercises make this book one that both novice and expert will come back to again and again.” Andrew Schofield, University of Birmingham // “This is a carefully planned and well-written book on modern physics of correlated electrons from one of the internationally recognized leaders in the field. Coleman manages to combine rigorous mathematical analysis with qualitative physics reasoning.” // Andrey Chubukov, University of Wisconsin // A modern, graduate-level introduction to many-body physics in condensed matter, this textbook explains the tools and concepts needed for a research-level understanding of the correlated behavior of quantum fluids. Starting
with an operator-based introduction to the quantum field theory of many-body physics, this textbook presents the Feynman diagram approach, Green’s functions, and finite-temperature many-body physics before developing the path integral approach to interacting systems. Special chapters are devoted to the concepts of Landau-Fermi liquid theory, broken symmetry, conduction in disordered systems, superconductivity, local moments and the Kondo effect, and the physics of heavy-fermion metals and Kondo insulators. A strong emphasis on concepts and numerous exercises make this an invaluable course book for graduate students in condensed matter physics. // It will also interest students in nuclear, atomic, and particle physics. // Piers Coleman is a Professor at the Center for Materials Theory at the Serin Physics Laboratory at Rutgers, State University of New Jersey. He invented the slave boson approach to strongly correlated electron systems and is fascinated by the emergent properties of quantum matter. Piers Coleman is also interested in science outreach and co-produced Music of the Quantum with his brother, the musician Jaz Coleman. // Cover illustration: “Big Bang Theory No. 2” courtesy of Swarez Modern Art Ltd. // Cambridge // UNIVERSITY PRESS www.cambridge.org // Cover designed by Hart McLeod Ltd // 9 // Pieface /rage xvii // Introduction ! // References 4 // 1 Scales and complexity 5 // 1.1 ?: Time scale 5 // 1.2 L: length scale 5 // 1.3 TV: particle number 7 // 1.4 C: complexity
and emergence 7 // References 9 // 2 Quantum fields 10 // 2.1 Overview j q // 2.2 Collective quantum fields I7 // 2.3 Harmonic oscillator: a zero-dimensional field theory 17 // 2.4 Collective modes: phonons 23 // 2.5 The thermodynamic limit: L -* 00 28 // 2.6 The continuum limit: a 0 31 // Exercises 37 // References 40 // 3 Conserved particles 42 // 3.1 Commutation and anticommutation algebras 43 // 3.1.1 Heuristic derivation for bosons 44 // 3.2 What about fermions? 45 // 3.3 Field operators in different bases 47 // 3.4 Fields as particle creation and annihilation operators 50 // 3.5 The vacuum and the many-body wavefunction 53 // 3.6 Interactions 55 // J.7 Equivalence with the many-body Schrödinger equation 60 // 3.8 Identical conserved particles in thermal equilibrium 62 // 3.8.1 Generalities 52 // 3.8.2 Identification of the free energy: key thermodynamic // properties 54 // 3.8.3 Independent particles 55 // Exercises 67 // References 69 // 4 Simple examples of second quantization 71 // 4.1 Jordan-Wigner transformation 71 // 4.2 The Hubbard model 78 // 4.3 Non-interacting particles in thermal equilibrium 80 // 4.3.1 Fluid of non-interacting fermions 81 // 4.3.2 Fluid of bosons: Bose-Einstein condensation 84 // Exercises 89 // References 93 // 5 Green’s functions 95 // 5.1 Interaction representation 96 // 5.1.1 Driven harmonic oscillator 100 // 5.1.2 Wick’s theorem and generating functionals 103 // 5.2 Green’s functions 106 // 5.2.1 Green’s function for free fermions
107 // 5.2.2 Green’s function for free bosons 110 // 5.3 Adiabatic concept 111 // 5.3.1 Gell-Mann-Low theorem 112 // 5.3.2 Generating function for free fermions 114 // 5.3.3 The spectral representation 118 // 5.4 Many-particle Green’s functions 121 // Exercises 124 // References 126 // 6 Landau Fermi-liquid theory 127 // 6.1 Introduction 127 // 6.2 The quasiparticle concept 129 // 6.3 The neutral Fermi liquid 133 // 6.3.1 Landau parameters 135 // 6.3.2 Equilibrium distribution of quasiparticles 138 // 6.4 Feedback effects of interactions 139 // 6.4.1 Renormalization of paramagnetism and compressibility by // interactions 143 // 6.4.2 Mass renormalization 145 // 6.4.3 Quasiparticle scattering amplitudes 148 // 6.5 Collective modes 150 // 6.6 Charged Fermi liquids: Landau-Silin theory 153 // 6.7 Inelastic quasiparticle scattering 157 // 6.7.1 Heuristic derivation 157 // 6.7.2 Detailed calculation of three-body decay process 158 // 6.7.3 Kadowaki-Woods ratio and “local Fermi liquids” 165 // 6.8 Microscopie basis of Fermi-liquid theory 168 // Exercises j 72 // References I74 // 7 Zero-temperature Feynman diagrams 175 // 7.1 Heuristic derivation 177 // 7.2 Developing the Feynman diagram expansion 183 // 7.2.1 Symmetry factors 189 // 7.2.2 Linked-cluster theorem 191 // 7.3 Feynman rules in momentum space 195 // 7.3.1 Relationship between energy and the S-matrix 197 // 7.4 Examples I99 // 7.4.1 Hartree-Fock energy 199 // 7.4.2 Exchange correlation 2OO // 7.4.3 Electron in a scattering
potential 202 // 7.5 The self-energy 206 // 7.5.1 Hartree-Fock self-energy 208 // 7.6 Response functions 210 // 7.6.1 Magnetic susceptibility of non-interacting electron gas 215 // 7.6.2 Derivation of the Lindhard function 218 // 7.7 The RPA (large-/V) electron gas 219 // 7.7.1 Jellium: introducing an inert positive background 221 // 7.7.2 Screening and plasma oscillations 223 // 7.7.3 The Bardeen-Pines interaction 225 // 7.7.4 Zero-point energy of the RPA electron gas 228 // Exercises 229 // References 232 // 8 Finite-temperature many-body physics 234 // 8.1 Imaginary time 236 // 8.1.1 Representations 236 // 8.2 Imaginary-time Green’s functions 239 // 8.2.1 Periodicity and antiperiodicity 240 // 8.2.2 Matsubara representation 241 // 8.3 The contour integral method 245 // 8.4 Generating function and Wick’s theorem 248 // 8.5 Feynman diagram expansion 251 // 8.5.1 Feynman rules from functional derivatives 253 // 8.5.2 Feynman rules in frequency-momentum space 254 // 8.5.3 Linked-cluster theorem 258 // 8.6 Examples of the application of the Matsubara technique 259 // 8.6.1 Hartree-Fock at a finite temperature 260 // 8.6.2 Electron in a disordered potential 260 // 8.7 Interacting electrons and phonons 268 // 8.7.1 o’2F: the electron-phonon coupling function 276 // 8.7.2 Mass renormalization by the electron-phonon interaction 280 // 8.7.3 Migdal’s theorem 284 // Appendix 8A Free fermions with a source term 287 // Exercises 288 // References 290 // 9 Fluctuation-dissipation theorem
and linear response theory 292 // 9.1 Introduction 292 // 9.2 Fluctuation-dissipation theorem for a classical harmonic // oscillator 294 // 9.3 Quantum mechanical response functions 296 // 9.4 Fluctuations and dissipation in a quantum world 297 // 9.4.1 Spectral decomposition I: the correlation function // S(t - t) 298 // 9.4.2 Spectral decomposition II: the retarded response function // XR(t - t) 298 // 9.4.3 Quantum fluctuation-dissipation theorem 300 // 9.4.4 Spectral decomposition III: fluctuations in imaginary // time 301 // 9.5 Calculation of response functions 301 // 9.6 Spectroscopy: linking measurement and correlation 305 // 9.7 Electron spectroscopy 308 // 9.7.1 Formal properties of the electron Green’s function 308 // 9.7.2 Tunneling spectroscopy 310 // 9.7.3 ARPES, AIPES, and inverse PES 313 // 9.8 Spin spectroscopy 315 // 9.8.1 DC magnetic susceptibility 315 // 9.8.2 Neutron scattering 315 // 9.8.3 Nuclear magnetic resonance 318 // 9.9 Electron transport spectroscopy 321 // 9.9.1 Resistivity and the transport relaxation rate 321 // 9.9.2 Optical conductivity 324 // 9.9.3 The f-sum rule 326 // Appendix 9A Kramers-Kronig relation 328 // Exercises 329 // References 331 // 10 Electron transport theory 332 // 10.1 Introduction 332 // 10.2 The Kubo formula 335 // 10.3 Drude conductivity: diagrammatic derivation 338 // 10.4 Electron diffusion 343 // 10.5 Anderson localization 347 // Exercises // References // 354 // 356 // 11 Phase transitions and broken symmetry 357
11.1 Order parameter concept 357 // 11.2 Landau theory 359 // 11.2.1 Field-cooling and the development of order 359 // 11.2.2 The Landau free energy 361 // 11.2.3 Singularities at the critical point 362 // 11.2.4 Broken continuous symmetries: the “Mexican hat” potential 364 // 11.3 Ginzburg-Landau theory I: Ising order 366 // 11.3.1 Non-uniform solutions of Ginzburg-Landau theory 367 // 11.4 Ginzburg-Landau II: complex order and superflow 372 // 11.4.1 A “macroscopic wavefunction” 372 // 11.4.2 Off-diagonal long-range order and coherent states 374 // 11.4.3 Phase rigidity and superflow 378 // 11.5 Ginzburg-Landau HI: charged fields 381 // 11.5.1 Gauge invariance 381 // 11.5.2 The Ginzburg-Landau equations 383 // 11.5.3 The Meissner effect 384 // 11.5.4 Vortices, flux quanta and type II superconductors 393 // 11.6 Dynamical effects of broken symmetry: the Anderson-Higgs mechanism 397 // 11.6.1 Goldstone mode in neutral superfluids 397 // 11.6.2 The Anderson-Higgs mechanism 399 // 11.6.3 Electro weak theory 402 // 11.7 The concept of generalized rigidity 406 // 11.8 Thermal fluctuations and criticality 406 // 11.8.1 Limits of mean-field theory: the Ginzburg criterion 410 // Exercises 412 // References 414 // 12 Path integrals 416 // 12.1 Coherent states and path integrals 416 // 12.2 Coherent states for bosons 419 // 12.2.1 Matrix elements and the completeness relation 420 // 12.3 Path integral for the partition function: bosons 424 // 12.3.1 Multiple bosons 427 // 12.3.2
Time-ordered expectation values 427 // 12.3.3 Gaussian path integrals 429 // 12.3.4 Source terms in Gaussian integrals 433 // 12.4 Fermions: coherent states and Grassman mathematics 435 // 12.4.1 Completeness and matrix elements 436 // 12.4.2 Path integral for the partition function: fermions 439 // 12.4.3 Gaussian path integral for fermions 444 // 12.5 The Hubbard-Stratonovich transformation 447 // 12.5.1 Heuristic derivation 447 // 12.5.2 Detailed derivation 450 // 12.5.3 Effective action 452 // 12.5.4 Generalizations to real variables and repulsive interactions 453 // Appendix 12A Derivation of key properties of bosonic coherent states 455 // Appendix 12B Grassman differentiation and integration 457 // Appendix 12C Grassman calculus: change of variables 458 // Appendix 12D Grassman calculus: Gaussian integrals 459 // Exercises 460 // References 462 // 13 Path integrals and itinerant magnetism 464 // 13.1 Development of the theory of itinerant magnetism 464 // 13.2 Path integral formulation of the Hubbard model 466 // 13.3 Saddle points and the mean-field theory of magnetism 469 // 13.4 Quantum fluctuations in the magnetization 477 // Exercises 482 // References 484 // 14 Superconductivity and BCS theory 486 // 14.1 Introduction: early history 486 // 14.2 The Cooper instability 490 // 14.3 The BCS Hamiltonian 496 // 14.3.1 Mean-field description of the condensate 498 // 14.4 Physical picture of BCS theory: pairs as spins 499 // 14.4.1 Nambu spinors 500 // 14.4.2 Anderson’s
domain-wall interpretation of BCS theory 502 // 14.4.3 The BCS ground state 505 // 14.5 Quasiparticle excitations in BCS theory 506 // 14.6 Path integral formulation 511 // 14.6.1 Mean-field theory as a saddle point of the path integral 512 // 14.6.2 Computing A and Tc 517 // 14.7 The Nambu-Gor’kov Green’s function 518 // 14.7.1 Tunneling density of states and coherence factors 523 // 14.8 Twisting the phase: the superfluid stiffness 531 // 14.8.1 Implications of gauge invariance 532 // 14.8.2 Calculating the phase stiffness 535 // Exercises 538 // References 540 // 15 Retardation and anisotropic pairing 542 // 15.1 BCS theory with momentum-dependent coupling 542 // 15.2 Retardation and the Coulomb pseudopotential 545 // 15.3 Anisotropie pairing 548 // 15.4 d-wave pairing in two-dimensions 553 // 15.5 Superfluid 3He 565 // 15.5.1 Early history: theorists predict a new superfluid 565 // 15.5.2 Formulation of a model 567 // 15.5.3 Gap equation 568 // Exercises 578 // References 580 // 16 Local moments and the Kondo effect 582 // 16.1 Strongly correlated electrons 582 // 16.2 Local moments 584 // 16.3 Asymptotic freedom in a cryostat: a brief history of the theory of // magnetic moments 585 // 16.4 Anderson’s model of local moment formation 587 // 16.4.1 The atomic limit 588 // 16.4.2 Virtual bound state formation: the non-interacting resonance 591 // 16.4.3 The Friedel sum rule 594 // 16.4.4 Mean-field theory 597 // 16.5 The Coulomb blockade: local moments in quantum dots
601 // 16.6 The Kondo effect 603 // 16.6.1 Adiabaticity and the Kondo resonance 606 // 16.7 Renormalization concept 609 // 16.8 Schrieffer-Wolff transformation 613 // 16.9 “Poor man’s” scaling 619 // 16.9.1 Kondo calculus: Abrikosov pseudo-fermions and the // Popov-Fedatov method 624 // 16.9.2 Universality and the resistance minimum 629 // 16.10 Nozičres Fermi-liquid theory 634 // 16.10.1 Strong-coupling expansion 634 // 16.10.2 Phase-shift formulation of the local Fermi liquid 636 // 16.10.3 Experimental observation of the Kondo effect 640 // 16.11 Multi-channel Kondo physics 641 // Appendix 16A Derivation of Kondo integral 645 // Exercises 647 // References 651 // 17 Heavy electrons 656 // 17.1 The Kondo lattice and the Doniach phase diagram 656 // 17.2 The Coqblin-Schrieffer model 663 // 17.2.1 Construction of the model 663 // 17.2.2 Enhancement of the Kondo temperature 666 // 17.3 Large-W expansion for the Kondo lattice 668 // 17.3.1 Preliminaries 668 // 17.4 The Read-Newns path integral 670 // 17.4.1 The effective action 674 // 17.5 Mean-field theory of the Kondo impurity 679 // 17.5.1 The impurity effective action 679 // 17.5.2 Minimization of free energy 683 // 17.6 Mean-field theory of the Kondo lattice 685 // 17.6.1 Diagonalization of the Hamiltonian 685 // 17.6.2 Mean-field free energy and saddle point 688 // 17.6.3 Kondo lattice Green’s function 691 // 17.7 Kondo insulators 693 // 17.7.1 Strong-coupling expansion 693 // 17.7.2 Large-TV treatment of the Kondo
insulator 695 // 17.8 The composite nature of the/-electron 697 // 17.8.1 A thought experiment: a Kondo lattice of nuclear spins 697 // 17.8.2 Cooper pair analogy 698 // 17.9 Tunneling into heavy-electron fluids 703 // 17.9.1 The cotunneling Hamiltonian 704 // 17.9.2 Tunneling conductance and the‘Tano lattice” 705 // 17.10 Optical conductivity of heavy electrons 709 // 17.10.1 Heuristic discussion 709 // 17.10.2 Calculation of the optical conductivity, including interband // term 710 // 17.11 Summary 714 // Exercises 714 // References 715 // 18 Mixed valence, fluctuations, and topology 720 // 18.1 The slave boson and mixed valence 721 // 18.2 Path integrals with slave bosons 723 // 18.2.1 The link between the Kondo and Anderson lattices 727 // 18.3 Fluctuations about the large-A limit 733 // 18.3.1 Effective action and Gaussian fluctuations 734 // 18.3.2 Fermi liquid interactions 739 // 18.4 Power-law correlations, Elitzur’s theorem, and the X-ray catastrophe 740 // 18.5 The spectrum of spin and valence fluctuations 744 // 18.6 Gauge invariance and the charge of the/-electron 747 // 18.7 Topological Kondo insulators 751 // 18.7.1 The rise of topology 752 // 18.7.2 The Z2 index 752 // 18.7.3 Topology: solution to the mystery of SmBe 753 // 18.7.4 The Shockley chain 757 // 18.7.5 Two dimensions: the spin Hall effect 761 // 18.7.6 Three dimensions and SmB 772 // 18.8 Summary 773 // Appendix 18A Fluctuation susceptibilities in the Kondo and infinite U // Anderson models 774
// Appendix 18B Elitzur’s theorem 778 // Exercises 780 // References 782 // Epilogue: the challenge of the future 787 // References 789 // Author Index 790 // Subject Index 792

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