LEADER 04780nam 22005535 450 001 9910970264203321 005 20250806174948.0 010 $a1-4612-0869-6 024 7 $a10.1007/978-1-4612-0869-3 035 $a(CKB)3400000000089298 035 $a(SSID)ssj0001243866 035 $a(PQKBManifestationID)11658381 035 $a(PQKBTitleCode)TC0001243866 035 $a(PQKBWorkID)11283631 035 $a(PQKB)10920991 035 $a(DE-He213)978-1-4612-0869-3 035 $a(MiAaPQ)EBC3073509 035 $a(PPN)238032396 035 $a(EXLCZ)993400000000089298 100 $a20121227d1994 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aInteracting Electrons and Quantum Magnetism /$fby Assa Auerbach 205 $a1st ed. 1994. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1994. 215 $a1 online resource (XIII, 255 p.) 225 1 $aGraduate Texts in Contemporary Physics 300 $aIncludes index. 311 08$a0-387-94286-6 311 08$a1-4612-6928-8 327 $aI Basic Models -- 1 Electron Interactions in Solids -- 2 Spin Exchange -- 3 The Hubbard Model and Its Descendants -- II Wave Functions and Correlations -- 4 Ground States of the Hubbard Model -- 5 Ground States of the Heisenberg Model -- 6 Disorder in Low Dimensions -- 7 Spin Representations -- 8 Variational Wave Functions and Parent Hamiltonians -- 9 From Ground States to Excitations -- III Path Integral Approximations -- 10 The Spin Path Integral -- 11 Spin Wave Theory -- 12 The Continuum Approximation -- 13 Nonlinear Sigma Model: Weak Coupling -- 14 The Nonlinear Sigma Model: Large N -- 15 Quantum Antiferromagnets: Continuum Results -- 16 SU(N) Heisenberg Models -- 17 The Large N Expansion -- 18 Schwinger Bosons Mean Field Theory -- 19 The Semiclassical Theory of the t ? J Model -- IV Mathematical Appendices -- Appendix A Second Quantization -- A.1 Fock States -- A.2 Normal Bilinear Operators -- A.3 Noninteracting Hamiltonians -- A.4 Exercises -- Appendix B Linear Response and Generating Functionals -- B.1 Spin Response Function -- B.2 Fluctuations and Dissipation -- B.3 The Generating Functional -- Appendix C Bose and Fermi Coherent States -- C.1 Complex Integration -- C.2 Grassmann Variables -- C.3 Coherent States -- C.4 Exercises -- Appendix D Coherent State Path Integrals -- D.1 Constructing the Path Integral -- D.2 Normal Bilinear Hamiltonians -- D.3 Matsubara Representation -- D.4 Matsubara Sums -- D.5 Exercises -- Appendix E The Method of Steepest Descents. 330 $aIn the excitement and rapid pace of developments, writing pedagogical texts has low priority for most researchers. However, in transforming my lecture l notes into this book, I found a personal benefit: the organization of what I understand in a (hopefully simple) logical sequence. Very little in this text is my original contribution. Most of the knowledge was collected from the research literature. Some was acquired by conversations with colleagues; a kind of physics oral tradition passed between disciples of a similar faith. For many years, diagramatic perturbation theory has been the major theoretical tool for treating interactions in metals, semiconductors, itiner­ ant magnets, and superconductors. It is in essence a weak coupling expan­ sion about free quasiparticles. Many experimental discoveries during the last decade, including heavy fermions, fractional quantum Hall effect, high­ temperature superconductivity, and quantum spin chains, are not readily accessible from the weak coupling point of view. Therefore, recent years have seen vigorous development of alternative, nonperturbative tools for handling strong electron-electron interactions. I concentrate on two basic paradigms of strongly interacting (or con­ strained) quantum systems: the Hubbard model and the Heisenberg model. These models are vehicles for fundamental concepts, such as effective Ha­ miltonians, variational ground states, spontaneous symmetry breaking, and quantum disorder. In addition, they are used as test grounds for various nonperturbative approximation schemes that have found applications in diverse areas of theoretical physics. 410 0$aGraduate Texts in Contemporary Physics 606 $aCondensed matter 606 $aCondensed Matter Physics 615 0$aCondensed matter. 615 14$aCondensed Matter Physics. 676 $a530.41 700 $aAuerbach$b Assa$4aut$4http://id.loc.gov/vocabulary/relators/aut$053952 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910970264203321 996 $aInteracting electrons and quantum magnetism$9188548 997 $aUNINA