Interacting Electrons and Quantum Magnetism

This book emphasizes the role that electron interactions play in the properties of condensed matter. It teaches the use of the powerful nonperturbative techniques that have become available in the last decades to discuss such topics as mixed valence systems, Kondo systems, heavy electrons, high-temperature copper oxide superconductors, the quantum Hall effect, and low-dimensional isotropic magnets.

Résumé
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.

Contenu
I 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.