This modern text describes the remarkable developments in quantum condensed matter physics following the experimental discoveries of quantum Hall effects and high temperature superconductivity in the 1980s. After a review of the phases of matter amenable to an independent particle description, entangled phases of matter are described in an accessible and unified manner. The concepts of fractionalization and emergent gauge fields are introduced using the simplest resonating valence bond insulator with an energy gap, the Z2 spin liquid. Concepts in band topology and the parton method are then combined to obtain a large variety of experimentally relevant gapped states. Correlated metallic states are described, beginning with a discussion of the Kondo effect on magnetic impurities in metals. Metals without quasiparticle excitations are introduced using the Sachdev-Ye-Kitaev model, followed by a discussion of critical Fermi surfaces and strange metals. Numerous end-of-chapter problems expand readers' comprehension and reinforce key concepts.

Table of Contents

1 Survey of Experiments

Part I Background

2 Fermi Liquid Theory

3 Dilute Bose Gas

4 Bardeen−Cooper−Schrieffer Theory of Superconductivity

5 Broken Symmetry and Superfluidity

6 Landau--Ginzburg Theory

7 Vortices in Superfluids and Superconductors

8 Boson Hubbard Model

9 Electron Hubbard Model

10 Relativistic Scalar Field: Diagrams

11 Relativistic Scalar Field: Correlation Functions

12 Fermions and Bosons in One Spatial Dimension

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 andU(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 Sachdev--Ye--Kitaev 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

About the Author

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.