Field Theories of Condensed Matter Physics

Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.1. Introduction; 2. The Hubbard model; 3. The magnetic instability of the Fermi system; 4. The renormalization group and scaling; 5. One-dimensional quantum antiferromagnets; 6. The Luttinger liquid; 7. Sigma models and topological terms; 8. Spin liquid states; 9. Gauge theory, dimer models, and topological phases; 10. Chiral spin states and anyons; 11. Anyon superconductivity; 12. Topology and quantum Hall effect; 13. The fractional quantum Hall effect; 14. Topological fluids; 15. Physics at the edge; 16. Topological insulators; 17. Quantum entanglement; References; Index.