Quantum Phase Transitions

Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory. Review of the first edition: 'Taken as a whole, this book is something of a theoretical masterpiece. With its tight organization, the book leads the determined (and theoretically inclined) reader on a tour encompassing some of the most challenging yet beautiful topics in contemporary theoretical physics ... Virtually every chapter contains a theoretical 'gem' ... The equations are manipulated with flair and elegance that are testimony to Sachdev's talent as one of the world's premier theorists.' Physics Today 'The book is well written from a pedagogical point of view and hence suitable for non-specialists. On the other hand, it can be used (some chapters) by graduate students as well.' Farruh Mukhamedov, Zentralblatt MATHPart I. Introduction: 1. Basic concepts; 2. Overview; Part II. A First Course: 3. Classical phase transitions; 4. The renormalization group; 5. The quantum Ising model; 6. The quantum rotor model; 7. Correlations, susceptibilities, and the quantum critical point; 8. Broken symmetries; 9. Boson Hubbard model; Part III. Non-zero Temperatures: 10. The Ising chain in a transverse field; 11. Quantum rotor models: large-N limit; 12. The d = 1, O(N => 3) rotor models; 13. The d = 2, O(N => 3) rotor models; 14. Physics close to and above the upper-critical dimension; 15. Transport in d = 2; Part IV. Other Models: 16. Dilute Fermi and Bose gases; 17. Phase transitions of Dirac fermions; 18. Fermi liquids, and their phase transitions; 19. Heisenberg spins: ferromagnets and antiferromagnets; 20. Spin chains: bosonization; 21. Magnetic ordering transitions of disordered systems; 22. Quantum spin glasses; References; Index.