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Auerbach A. — Interacting electrons and quantum magnetism
Auerbach A. — Interacting electrons and quantum magnetism



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Название: Interacting electrons and quantum magnetism

Автор: 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: en

Рубрика: Физика/Физика твёрдого тела/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1994

Количество страниц: 255

Добавлена в каталог: 26.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$CP^{n-1}$ models      153
$CP^{N-1}$ models, large N      155
$\beta$ function      147
$\theta$ term      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$\acute{e}$el field      130
N$\acute{e}$el gauge field      154 177 219 221
N$\acute{e}$el state      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$\ddot{o}$dinger equation      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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