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Auerbach A. — Interacting electrons and quantum magnetism
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Название: Interacting electrons and quantum magnetismАвтор: Auerbach A. Аннотация: This is a textbook on quantum magnetism and on modern techniques in strongly correlated electron systems. It explains concepts and techniques that are useful in widely diverse areas such as quantum spin systems, the fractional quantum Hall effect, superfluidity, and high-temperature superconductivity. The book starts with interactions between electrons and spin exchange; the Heisenberg and t-J models are derived from the Hubbard model, and itinerant magnetism is presented as a variational theory. Superconductivity and charge ordering in the negative-U Hubbard model are described by pseudospins. The Heisenberg model is used to elucidate general concepts such as spontaneous symmetry breaking, Goldstone modes and spin waves, thermal and quantum disorder in low dimensions, Haldane's gap. The text emphasizes nonperturbative approaches: ground state theorems, variational wavefunctions, parent Hamiltonians, single mode excitations, the spin path integral and its large-S expansion, Haldane's mapping, Polyakov's weak-coupling renormalization, large-N expansions for constrained systems, and the semiclassical theory of the t-J model. Mathematical derivations are self contained. Appendices provide standard many-body tools including second quantization, Grassmann variables, generating functionals, linear response, correlation functions, Fermi and Bose coherent-states path integrals, Matsubara representation, and the method of steepest descents. There are guided bibliographies and exercises at the end of chapters.
Язык: Рубрика: Физика /Физика твёрдого тела /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1994Количество страниц: 255Добавлена в каталог: 26.07.2005Операции: Положить на полку |
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Предметный указатель
153 155 147 159 Adiabatic approximation 213 Aharonov — Bohm phase 161 AKLT Hamiltonians 85 Annihilation operator 225 Band structure 3 Berry phase 103 133 216 Berry phase, topological 133 Bilinear Hamiltonians, generating functionals 242 Bilinear operators 227 Bipartite lattice 29 Bogoliubov inequality 64 Bogoliubov transformation 124 194 Bohr — Sommerfeld quantization 110 Bose coherent states 237 Bose condensation 190 199 Canting field 130 Cauchy — Schwartz inequality 63 Coherent states, Bose 239 Coherent states, Fermi 239 Coherent states, spin 72 101 Conjugate representation 168 Consite fluctuations 183 Consite fluctuations, renormalized classical 164 Consite fluctuations, spin 64 172 Consite fluctuations, sum rules 181 Constrained fermions 168 Constraint field 154 170 Constraints, holonomic 206 Continuum approximation 159 Continuum hamiltonian 131 continuum limit 139 Correlation function, dynamical structure factor 93 233 Correlation function, dynamical susceptibility 246 Correlation function, mean field theory 197 Correlation function, Ornstein — Zernicke 148 correlation length 131 135 140 149 162 192 203 Coulomb interaction 4 6 21 Creation operator 225 Cutoff scale 131 Density fluctuations 23 des Cloizeaux and Pearson excitations 59 Dimer states 83 Doped antiferromagnet 205 Effective Hamiltonian 26 Elementary excitations 94 Fermi energy 3 Fermi surface 3 Fermi surface nesting 44 Ferrimagnet 126 Field operator 4 Fixed points 148 Fluctuation-dissipation theorem 233 Fock states 3 225 Free energy, noninteracting 243 Frustration 113 Gauge field 176 Gauge freedom 72 Gauge potentials 143 Gauge symmetry 145 Gaussian contractions 180 Gaussian Integrals 251 Generating functional 170 234 Generating functional, coherent states 170 Generating Hamiltonian 169 Goldstone’s theorem 95 Grassmann integration 238 Grassmann variables 208 237 Green’s function 105 Ground state, antiferromagnet 52 Ground state, ferromagnet 56 Ground state, Schwinger bosons mean field 195 Ground state, variational theorem 39 Gutzwiller projection 196 Gutzwiller states 45 Haar measure 73 Haldane gap 59 67 96 162 Haldane — Shastry model 45 Haldane’s mapping 130 Half-odd integer spins 56 160 161 Hartree — Fock equations 39 Hedgehogs 163 Heisenberg ferromagnet, classical 192 Heisenberg model 8 51 Holstein and Primakoff operators 69 Hopping matrix elements 23 Hubbard model 8 21 Hubbard model, negative-U 28 Hubbard model, two-dimensional 205 Hubbard — Stratonovich fields 176 Hubbard — Stratonovich identity 171 Infrared divergence 142 Interactions, irrelevant 7 Interactions, marginal 7 Ising configurations 52 Itinerant magnetism 44 Kosterlitz — Thouless temperature 147 Kramers — Kronig relations 233 Lagrangian, normal 171 Lagrangians, anomalous 172 Large N approximations 165 173 Large N expansion 175 Lattice Laplacian 118 Laughlin state 91 Lieb, Schultz and Mattis Theorem 57 201 Lieb’s Theorem, Hubbard model 47 Linked cluster theorem 181 Local density 5 Long range order 62 126 198 Long range order, quasi 62 Magnetic bands 42 Majumdar — Ghosh hamiltonian 83 Marshall’s theorem 53 Matsubara frequencies 117 234 244 Mean field equations 175 Mermin and Wagner’s Theorem 62 126 Monopole vector potential 104 208 Mott insulator 27 205 N 130 N 154 177 219 221 N 52 Nagaoka’s Theorem 45 Nonlinear sigma model 135 Nonlinear sigma model, large N 153 Nonlinear sigma model, weak coupling 139 Normal ordering 239 Ordered moment 202 Ornstein — Zernicke correlations 148 193 Path integral, Bose coherent states 116 Path integral, coherent state 241 Path integral, imaginary time 129 Path integral, phase-space 115 Path integral, spin 101 Path integral, t — J model 209 Polaron hopping 217 Pontryagin index 159 Pseudo-spin 30 Quantum disorder 66 Quantum Hall effect 91 97 Quantum Heisenberg Model 27 Quantum Monte Carlo simulations 243 Renormalization 7 Renormalization, one loop level 144 Renormalization, poor man’s 147 151 Resolution of identity 73 Resolution of identity, spin-hole coherent states 209 Resolvent operator 25 Resonating valence bond states 80 84 Response function 231 RPA propagator 179 252 Saddle point equations 175 251 Saddle point expansion 249 Schr 3 Schwinger boson mean field state 81 Schwinger bosons 70 206 Schwinger bosons mean field theory, antiferromagnet 194 Schwinger bosons mean field theory, ferromagnet 187 Schwinger bosons, antiferromagnet 166 Schwinger bosons, ferromagnet 166 screening 4 Second quantization 225 Semiclassical approximation 106 Semiclassical configurations 129 Semiclassical spectrum 109 Short-range interactions 63 Single mode approximation 93 Slave fermion 206 Solitons 140 Spin coherent states 207 Spin density wave 40 Spin exchange 11 Spin exchange, antiferromagnetic 13 Spin exchange, ferromagnetic 11 Spin exchange, intersite 23 Spin exchange, superexchange 18 Spin liquids 82 88 164 Spin operators 227 Spin polaron 212 Spin wave fluctuations 142 Spin wave theory 113 Spin wave velocity 134 202 Spin waves, antiferromagnet 125 Spin waves, ferromagnet 119 122 190 Spin-flop transition 33 Spin-hole coherent states 208 Spiral states 41 Spontaneously broken symmetry 61 Stationary phase approximation 249 Steepest descents method 249 Stiffness constant 132 203 Stoner’s criterion 43 Superconductivity 30 220 Superconductivity, high-temperature 205 Superexchange 18 27 31 Superexchange path 19 Supersolid 33 susceptibility 43 63 132 190 191 235 t — J model 25 205 t — J model, classical Hamiltonian 210 t — J model, spin 5 207 Time ordered exponential 231 241 Tunneling, multidimensional 214 222 Tunneling, path 215 Tunneling, spin 214 Universality 147 Valence bond solids 85 Valence bond states 79 Wannier states 22 Winding number 159 XY model 146 151
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