The Hubbard model
The magnetic instability of the Fermi system
The renormalization group and scaling
One-dimensional quantum antiferromagnets
The Luttinger liquid
Sigma models and topological terms
Spin-liquid states
Gauge theory, dimer models, and topological phases
Chiral spin states and anyons
Anyon superconductivity
Topology and quantum Hall effect
The fractional quantum Hall effect
Topological fluids
Physics at the edge
Topological insulators
Quantum entanglement

"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"