Field Theories for Low-Dimensional Condensed Matter Systems: Spin Systems and Strongly Correlated ElectronsGuiseppe Morandi Springer Science & Business Media, 26 ביולי 2000 - 275 עמודים This book is especially addressed to young researchers in theoretical physics with a basic background in Field Theory and Condensed Matter Physics. The topics were chosen so as to offer the largest possible overlap between the two expertises, selecting a few key problems in Condensed Matter Theory which have been recently revisited within a field-theoretic approach. The presentation of the material is aimed not only at providing the reader with an overview of this exciting frontier area of modern theoretical physics, but also at elucidating most of the tools needed for a technical comprehen sion of the many papers appearing in current issues of physics journals and, hopefully, to enable the reader to tackle research problems in this area of physics. This makes the material a live creature: while not pretending it to be exhaustive, it is tutorial enough to be useful to young researchers as a starting point in anyone of the topics covered in the book. |
תוכן
1 Introduction | 1 |
References | 5 |
2 Fermi Liquids and Luttinger Liquids | 9 |
221 The Fermi Gas | 10 |
222 Landaus Theory of Fermi Liquids | 12 |
223 Microscopic Basis of Landaus Theory | 17 |
224 Summary | 21 |
23 Renormalization Group for Interacting Fermions | 22 |
52 Quantum Magnetism | 150 |
522 Spin Path Integral | 151 |
523 Spin Wave Theory | 153 |
524 Continuum Theory for Anisotropic Models | 155 |
525 Anisotropic Quantum Rotators | 157 |
526 Haldancs Mapping | 159 |
527 Spin Liquid States | 160 |
53 Pseudospins and Superconductivity | 161 |
231 One Dimension | 23 |
232 Two and Three Dimensions | 28 |
24 Bosonization and the Luttinger Liquid | 32 |
the Concept of the Luttinger Liquid | 39 |
243 Summary | 47 |
251 Transport | 48 |
252 Disorder | 53 |
253 The Spin12 Chain as a Luttinger Liquid | 59 |
26 Spin Ladders and Coupled Luttinger Liquids | 69 |
262 Two Coupled Luttinger Liquids | 71 |
263 Summary | 74 |
When to Bosonize in Peace | 75 |
References | 77 |
Quantum Number Fractionalization in Antiferromagnets | 83 |
32 HaldaneShastry Hamiltonian | 84 |
33 Ground State | 85 |
34 Spinons | 90 |
35 Annihilation Operators | 98 |
36 Spin Current | 102 |
37 Supersymmetry | 104 |
38 Holons | 106 |
Fourier Sums | 111 |
Problems | 112 |
References | 115 |
Conformal Field Theory Approach to Quantum Impurity Problems | 117 |
411 Reduction to ID | 118 |
412 Perturbative RG | 119 |
413 Local Fermi Liquid Theory | 120 |
42 Some Basic Conformal Field Theory Luttinger Liquid Techniques | 124 |
43 CFT Approach to the Kondo Problem | 132 |
432 BCFT and the MultiChannel Kondo Problem | 136 |
References | 141 |
5 Quantum Magnetism Approaches to Strongly Correlated Electrons | 143 |
511 TwoSite Hubbard Model | 144 |
512 Renormalization to Low Energy Subspace | 145 |
513 From Hubbard to t J and Heisenberg Models | 147 |
514 The Negative Hubbard Model | 149 |
531 Charge Density Wave to Superconductivity | 162 |
532 Order of Transition from Rotator Theory | 163 |
533 SO5 Rotator Theory and HighTc Superconductors | 165 |
534 Vortex Dynamics in Superfluids | 167 |
References | 170 |
Introduction to Some Common Topics in Gauge Theory and Spin Systems | 171 |
62 What Is a Gauge Theory? | 173 |
621 Electrodynamics | 174 |
622 Geometry | 180 |
623 Schrodinger Equation for a Charged Particle | 183 |
624 BohmAharonov Phase | 185 |
625 Classical YangMills Theory | 186 |
63 Relativistic Fermions | 191 |
631 1 + 1 Dimensions | 195 |
632 2+1 Dimensions | 198 |
633 3+1 Dimensions | 200 |
64 Quantized YangMills Theory | 202 |
641 Canonical Quantization of Electrodynamics | 207 |
642 Path Integrals | 209 |
65 Quantum Spins and Strong Coupling in Gauge Theory | 211 |
66 Staggered Fermions | 216 |
67 Strong Coupling Lattice Gauge Theory | 220 |
672 Strong Coupling | 222 |
68 Results on Strong Coupling | 228 |
References | 231 |
Quantum Chaos and Transport in Mesoscopic Systems | 235 |
72 Quantum Chaos | 236 |
721 Beyond Random Matrix Theory | 241 |
722 From Disordered to Chaotic Systems | 244 |
73 Quantum Dots | 249 |
732 Orthodox Theory | 251 |
733 Od Hamiltonian | 254 |
74 Quasiparticle Lifetime in a Finite System | 257 |
741 Transition Region | 261 |
References | 267 |
271 | |
מהדורות אחרות - הצג הכל
מונחים וביטויים נפוצים
algebra antiferromagnet B.L. Altshuler boson boundary conditions charge and spin chiral symmetry classical Condensed Matter conformal field theory consider constant constraint continuum correlation functions corresponding decay defined degrees of freedom density diagonal diagram dimensional dimensions Dirac disordered dynamical Editors effective eigenstates eigenvalues electron energy equation excitations Fermi liquid Fermi surface field theory finite fixed point flavours fluctuations gauge field gauge group gauge invariant gauge transformations ground H.J. Schulz Hamiltonian Heisenberg Hubbard model impurity interaction Landau's theory lattice gauge theory Lett linear Luttinger liquid magnetic field matrix momentum noninteracting obtained one-dimensional orbitals parameter particle path integral phase Phys Physics Poisson brackets potential properties quantization quantum Hall quasiparticle relativistic renormalization group representation scattering singlet spacetime spectrum spin systems spinless spinon spinor Statistical strong coupling limit superconducting symmetry breaking temperature tensor term vector wave-function Yang-Mills zero