Quantum Phases of Matter

Subir Sachdev is the Herchel Smith Professor of Physics at Harvard University. He has also held professional positions at Bell Labs and Yale University. He has been elected to national academies of science in India and the US and is a recipient of several prestigious awards, including the Dirac Medal from the International Centre for Theoretical Physics, and the Lars Onsager Prize from the American Physical Society.

'A visionary, provocative, and thoughtful text: Sachdev's narrative ties his intellectual motivation to a set of striking emergent phenomena observed in experiments on well-characterized quantum materials and devices. It explores modern topics from a systematic and unified perspective based on effective field theories. The derivations give plenty of intuitive guidance to make the physical meaning of each transformation transparent for student or expert. The author covers a broad swath of the intellectual framework that underlies many of the most interesting contemporary developments in condensed matter theory.' Steven Kivelson, Stanford University

• Preface; 1. Survey of experiments; Part I: Background: 2. Fermi liquid theory; 3. Dilute Bose gas; 4. BCS theory of superconductivity; 5. Broken symmetry and superfluidity; 6. Landau–Ginzburg theory; 7. Vortices in superfluids; 8. Boson Hubbard model; 9. Electron Hubbard model; 10. Relativistic scalar field: diagrams; 11. Relativistic scalar field: correlation functions; 12. Fermions and bosons; Part II. Fractionalization and Emergent Gauge Fields I: 13. Introduction to gapped spin liquids; 14. Fractionalization in the XY model in 2+1 dimensions; 15. Theory of gapped Z2 spin liquids; 16. Z2 gauge theory; 17. Chern–Simons gauge theories; Part III. Band Topology: 18. Berry phases and Chern numbers; 19. Integer quantum Hall states; 20. Topological insulators and superconductors; Part IV. Fractionalization and Emergent Gauge Fields II: 21. Parton theories; 22. The chiral spin liquid; 23. Non-Abelian Ising anyons; 24. Fractional quantum hall states; 25. Dualities of XY models and U(1) gauge theories; 26. Applications of dualities to spin liquids; 27. Boson–fermion and fermion–fermion dualities; 28. Gapless spin liquids; Part V. Correlated Metals: 29. Kondo impurity model; 30. The heavy Fermi liquid; 31. The fractionalized Fermi liquid; 32. SYK models; 33. Random quantum spin liquids and spin glasses; 34. Fermi surfaces without quasiparticles; Appendix A. coherent state path integral; Appendix B. Grassman path integral; Appendix C. From spin Berry phases to background gauge charges; Appendix D. Emergent Z2 gauge theories; References; Index.