Advanced Quantum Condensed Matter Physics
One-Body, Many-Body, and Topological Perspectives

Condensed matter physics has fast become the largest discipline within physics. Based on an established course, this comprehensive textbook covers one-body, many-body and topological perspectives. It is the first textbook that presents a comprehensive coverage of topological aspects of condensed matter as a distinct yet integrated component. It covers topological fundamentals and their connection to physics, introduces Berry phase and Chern numbers, describes general topological features of band structures and delineates its classification. Applications as manifest in the quantum Hall effect, topological insulators and Weyl semimetal are presented. Modern topics of current interest are explored in-depth, helping students prepare for cutting-edge research. These include one-electron band theory, path integrals and coherent states functional integrals as well as Green and Matsubara functions, spontaneous symmetry breaking, superfluidity and superconductivity. Multiple chapters covering quantum magnetism are also included. With end-of-chapter exercises throughout, it is ideal for graduate students studying advanced condensed matter physics.

Preface; Part I. One-Electron Theory: 1. Preliminaries; 2. Electrons and band theory: formalism in the one-electron approximation; 3. Electrons and band theory: methods of energy-band calculations; 4. Electrons and band theory: effects of spin-orbit interactions; 5. Linear response and the dielectric function; 6. Phonons and lattice dynamics; 7. Dimensionality, susceptibility and instabilities; Part II. Topological Phases: 8. Topological aspects of condensed matter physics: a historical perspective; 9. Topological preliminaries; 10. Berry-ology; 11. Topological aspects of insulator band structure and early discoveries; 12. Dirac materials and Dirac fermions; Part III. Many-Body Physics: 13. Many-body physics and second quantization; 14. The interacting electron gas; 15. Green functions for many-body systems and Feynman diagrams; 16. Path integrals; 17. Boson systems: Bose-Einstein condensation and superfluidity; 18. Landau Fermi liquid theory; 19. Non-Fermi liquids, the Luttinger liquid and bosonization; 20. Electron-Phonon interactions; 21. Microscopic theory of conventional superconductivity; 22. Quantum theory of magnetism: exchange coupling mechanisms; 23. Quantum theory of magnetism: magnetic insulator groundstates and spin-wave excitations; 24. Quantum theory of magnetism: itinerant-electron systems and Kondo effect; References; Index.

Michael El-Batanouny is a Professor of Physics at Boston University. He is the author of Symmetry and Condensed Matter Physics: A computational approach (Cambridge, 2008). His research area is in surface physics, where he has an international reputation in the topics of nonlinear surface physics, surface dynamics, surface magnetism, and more recently, in topological aspects of surfaces, especially in electron-phonon related phenomena.