Interacting Electrons and Quantum MagnetismIn the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner ant magnets, and superconductors. It is in essence a weak coupling expan sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics. |
Contents
III | 3 |
IV | 4 |
V | 6 |
VI | 7 |
VII | 8 |
VIII | 11 |
X | 13 |
XI | 16 |
LXIX | 136 |
LXX | 139 |
LXXI | 141 |
LXXII | 142 |
LXXIII | 147 |
LXXIV | 150 |
LXXV | 153 |
LXXVI | 155 |
XII | 19 |
XIII | 21 |
XIV | 22 |
XV | 25 |
XVI | 28 |
XVII | 30 |
XVIII | 33 |
XIX | 37 |
XX | 39 |
XXI | 40 |
XXII | 45 |
XXIII | 48 |
XXIV | 51 |
XXV | 52 |
XXVI | 56 |
XXVII | 59 |
XXVIII | 61 |
XXIX | 62 |
XXX | 66 |
XXXI | 68 |
XXXII | 69 |
XXXIV | 70 |
XXXV | 72 |
XXXVII | 75 |
XXXIX | 79 |
XL | 81 |
XLI | 83 |
XLII | 84 |
XLIII | 85 |
XLIV | 87 |
XLV | 88 |
XLVI | 93 |
XLVII | 94 |
XLVIII | 95 |
XLIX | 96 |
L | 99 |
LI | 101 |
LII | 105 |
LIV | 107 |
LV | 108 |
LVI | 110 |
LVII | 113 |
LVIII | 118 |
LIX | 119 |
LX | 120 |
LXI | 121 |
LXII | 123 |
LXIII | 126 |
LXIV | 129 |
LXV | 130 |
LXVI | 131 |
LXVII | 133 |
LXXVII | 157 |
LXXVIII | 159 |
LXXIX | 162 |
LXXX | 163 |
LXXXI | 165 |
LXXXII | 166 |
LXXXIII | 167 |
LXXXIV | 168 |
LXXXV | 169 |
LXXXVI | 171 |
LXXXVII | 172 |
LXXXVIII | 175 |
LXXXIX | 176 |
XC | 178 |
XCI | 181 |
XCII | 182 |
XCIII | 183 |
XCIV | 186 |
XCV | 187 |
XCVI | 191 |
XCVII | 192 |
XCVIII | 194 |
XCIX | 198 |
C | 200 |
CI | 201 |
CII | 203 |
CIII | 205 |
CV | 206 |
CVI | 207 |
CVII | 211 |
CVIII | 214 |
CIX | 218 |
CX | 220 |
CXI | 221 |
CXII | 223 |
CXIII | 225 |
CXV | 226 |
CXVI | 227 |
CXVII | 228 |
CXVIII | 231 |
CXIX | 233 |
CXXI | 237 |
CXXII | 239 |
240 | |
CXXIV | 241 |
CXXV | 242 |
CXXVI | 244 |
CXXVIII | 246 |
CXXIX | 249 |
253 | |
Other editions - View all
Common terms and phrases
antiferromagnet approximation Auerbach Berry phase bibliography Bose broken symmetry Chapter classical configurations constraint continuum correlation function correlation length defined derive diagrams dimensions effective eigenvalues electrons equations evaluated excitations expansion expectation value Fermi fermions ferromagnetic finite temperatures Fock gauge field given Green's function Haldane's half filling half-odd integer spins Hamiltonian Heisenberg antiferromagnet Heisenberg model hole hopping Hubbard model interactions Lett long-range order magnetic Matsubara mean field theory Mermin and Wagner's momentum nearest neighbor NĂ©el negative-U NLSM nonlinear sigma model obtain parameters path integral Phys polaron quantum Heisenberg renormalization representation rotational saddle point SBMFT Schwinger bosons Section semiclassical spin coherent spin correlations spin fluctuations spin operators spin wave spin wave theory Stot SU(N sublattices subspace superconductivity t-J model total spin transformation valence bond vanish variables variational vector Wagner's Theorem wave function yields