Preface |
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xiii | |
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1 | (20) |
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1.1 Metals and Band Insulators |
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1 | (3) |
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4 | (4) |
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8 | (5) |
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1.4 The Heavy-Fermion Intermetallic Compounds |
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13 | (1) |
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14 | (7) |
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21 | (12) |
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21 | (1) |
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2.2 Interacting-Electron Gas |
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22 | (3) |
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25 | (1) |
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26 | (1) |
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2.5 Dynamic Response Functions |
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27 | (1) |
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2.6 Green's Functions and Quasiparticle Lifetime |
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28 | (4) |
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32 | (1) |
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33 | (10) |
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33 | (4) |
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3.2 Off-Diagonal Long-Range Order |
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37 | (1) |
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38 | (2) |
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40 | (3) |
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4 Bardeen---Cooper---Schrieffer Theory of Superconductivity |
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43 | (10) |
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43 | (2) |
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4.2 Off-Diagonal Long-Range Order |
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45 | (2) |
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47 | (2) |
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49 | (3) |
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52 | (1) |
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5 Broken Symmetry and Superfluidity |
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53 | (6) |
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5.1 Ising Model and Surface Tension |
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54 | (1) |
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5.2 XY Model and Helicity Modulus |
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55 | (1) |
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5.3 Superconductors and Gauge Invariance |
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56 | (1) |
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57 | (1) |
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58 | (1) |
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6 Landau--Ginzburg Theory |
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59 | (7) |
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6.1 Hubbard--Stratonovich Transformation |
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59 | (2) |
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61 | (2) |
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6.3 Effective Classical Theory |
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63 | (1) |
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64 | (1) |
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64 | (1) |
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65 | (1) |
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7 Vortices in Superfluids and Superconductors |
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66 | (8) |
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66 | (3) |
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69 | (2) |
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71 | (1) |
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72 | (1) |
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73 | (1) |
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74 | (13) |
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75 | (1) |
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76 | (3) |
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8.3 Continuum Quantum Field Theories |
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79 | (4) |
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8.4 Insulators at Non-Integer Filling |
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83 | (1) |
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84 | (3) |
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87 | (27) |
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9.1 The Superexchange Interaction |
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89 | (2) |
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9.2 Insulating Antiferromagnets and Hard-Core Bosons |
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91 | (5) |
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9.3 The t--J Model and d-Wave Pairing |
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96 | (4) |
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9.4 Paramagnon Theory of Antiferromagnetic Metals |
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100 | (10) |
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110 | (4) |
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10 Relativistic Scalar Field: Diagrams |
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114 | (8) |
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115 | (3) |
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10.2 Expansion for Susceptibility |
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118 | (3) |
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121 | (1) |
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11 Relativistic Scalar Field: Correlation Functions |
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122 | (11) |
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11.1 Spectral Representation |
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122 | (5) |
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11.2 Correlations across the Quantum Critical Point |
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127 | (5) |
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132 | (1) |
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12 Fermions and Bosons in One Spatial Dimension |
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133 | (20) |
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12.1 Non-interacting Fermions |
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134 | (9) |
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12.2 Interacting Fermions |
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143 | (3) |
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12.3 Bosons in One Dimension |
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146 | (3) |
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149 | (4) |
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Part II Fractionalization and emergent gauge fields I |
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13 Introduction to Gapped Spin Liquids |
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153 | (10) |
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155 | (1) |
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13.2 Topological Properties |
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155 | (1) |
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13.3 Emergent Gauge Fields |
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156 | (3) |
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13.4 Excitations of the Spin Liquid |
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159 | (4) |
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14 Fractionalization in the XY Model in 2+1 Dimensions |
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163 | (13) |
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14.1 The Conventional XY Model |
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164 | (1) |
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14.2 The Extended XY Model |
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165 | (10) |
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175 | (1) |
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15 Theory of Gapped Z2 Spin Liquids |
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176 | (20) |
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177 | (3) |
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180 | (3) |
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183 | (5) |
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15.4 Dynamics of Excitations |
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188 | (6) |
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194 | (2) |
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196 | (25) |
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16.1 From the Large-N Path Integral to a Z2 Gauge Theory |
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196 | (3) |
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16.2 Hamiltonian of the Z2 Gauge Theory |
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199 | (4) |
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16.3 Topological Order at Small g |
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203 | (3) |
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206 | (3) |
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16.5 Visons and Anyon Condensation |
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209 | (5) |
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16.6 Models of Rydberg Atoms |
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214 | (5) |
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219 | (2) |
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17 Chern---Simons Gauge Theories |
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221 | (14) |
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17.1 Chern--Simons Theory on a Torus |
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222 | (3) |
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17.2 Quasiparticles and Their Statistics |
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225 | (1) |
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17.3 Coupling to an External Gauge Field |
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226 | (1) |
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227 | (4) |
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231 | (4) |
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18 Berry Phases and Chern Numbers |
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235 | (11) |
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235 | (2) |
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18.2 Berry Phase of a Spin |
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237 | (2) |
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18.3 Berry Curvature of Bloch Bands |
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239 | (4) |
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243 | (1) |
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244 | (2) |
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19 Integer Quantum Hall States |
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246 | (10) |
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19.1 Non-relativistic Particles |
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246 | (3) |
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19.2 Relativistic Particles (Graphene) |
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249 | (1) |
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250 | (4) |
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19.4 Anomaly Inflow Arguments |
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254 | (1) |
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255 | (1) |
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20 Topological Insulators and Superconductors |
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256 | (13) |
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20.1 Su--Schrieffer--Heeger Model |
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257 | (4) |
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20.2 Kane--Mele Insulators |
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261 | (1) |
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20.3 Odd-Parity Superconductors |
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262 | (7) |
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Part IV Fractionalization and emergent gauge fields II |
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269 | (5) |
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21.1 Spin Fractionalization into Bosonic Partons |
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269 | (1) |
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21.2 Spin Fractionalization into Fermionic Partons |
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270 | (2) |
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272 | (1) |
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272 | (2) |
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22 The Chiral Spin Liquid |
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274 | (6) |
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275 | (1) |
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276 | (1) |
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277 | (1) |
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278 | (2) |
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23 Non-Abelian Ising Anyons |
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280 | (7) |
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23.1 Visons and Majorana Zero Modes |
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281 | (3) |
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23.2 Non-Abelian Statistics |
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284 | (2) |
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23.3 Connections to Odd-Parity Superconductors |
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286 | (1) |
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24 Fractional Quantum Hall States |
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287 | (8) |
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287 | (3) |
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24.2 Edge Theory of the Fractional Quantum Hall States |
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290 | (2) |
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24.3 Bulk Gauge Theory of the Fractional Quantum Hall States |
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292 | (2) |
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294 | (1) |
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25 Dualities of XY Models and U(1) Gauge Theories |
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295 | (17) |
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295 | (2) |
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25.2 Vortices in the XY Model in D = 2 |
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297 | (7) |
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25.3 U(1) Gauge Theory with Monopoles in D = 3 |
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304 | (2) |
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25.4 Particle-Vortex Duality of the XY model in D = 3 |
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306 | (5) |
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311 | (1) |
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26 Applications of Dualities to Spin Liquids |
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312 | (16) |
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312 | (7) |
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26.2 Gapped Z2 Spin Liquids |
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319 | (9) |
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27 Boson--Fermion and Fermion-Fermion Dualities |
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328 | (12) |
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27.1 Fermion--Boson Duality I |
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328 | (5) |
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27.2 Fermion--Boson Duality II |
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333 | (1) |
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27.3 Fermion--Fermion Duality |
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334 | (3) |
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27.4 Fractional Quantum Hall Effect: Dirac Composite Fermions |
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337 | (3) |
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340 | (11) |
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28.1 U(1) Spin Liquids on the Square Lattice: Bosonic Spinons |
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341 | (3) |
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28.2 U(1) Spin Liquids on the Square Lattice: Fermionic Spinons |
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344 | (1) |
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28.3 Gapless SU(2) Spin Liquids |
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344 | (2) |
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28.4 Gapless Z2 Spin Liquid on the Square Lattice |
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346 | (5) |
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351 | (17) |
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29.1 Resonant-Level Model |
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351 | (3) |
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354 | (1) |
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29.3 Renormalization Theory |
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355 | (4) |
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359 | (3) |
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362 | (4) |
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366 | (2) |
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30 The Heavy Fermi Liquid |
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368 | (13) |
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30.1 The Kondo Lattice Heavy Fermi Liquid |
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369 | (4) |
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30.2 The Luttinger Relation |
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373 | (8) |
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31 The Fractionalized Fermi Liquid |
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381 | (25) |
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31.1 The FL State in the Kondo Lattice |
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383 | (3) |
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31.2 Emergent Gauge Fields and Generalized Luttinger Relations |
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386 | (2) |
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31.3 Torus Flux Insertion and Generalized Luttinger Relations |
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388 | (7) |
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31.4 The FL State in the Single-Band Hubbard Model |
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395 | (11) |
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32 Sachdev--Ye--Kitaev Models |
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406 | (26) |
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32.1 Random Matrix Model: Free Fermions |
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407 | (5) |
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32.2 Large-N Theory of the SYK Model |
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412 | (13) |
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32.3 G--Σ Effective Action |
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425 | (6) |
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431 | (1) |
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33 Random Quantum Spin Liquids and Spin Glasses |
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432 | (19) |
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33.1 Classical Ising Spin Glass |
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433 | (2) |
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33.2 Quantum Rotor Spin Glass |
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435 | (6) |
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33.3 Random Heisenberg Magnet |
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441 | (10) |
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34 Fermi Surfaces without Quasiparticles |
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451 | (37) |
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34.1 Onset of Ising Ferromagnetism |
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452 | (9) |
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461 | (1) |
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34.3 Fermi Surface Coupled to a Gauge Field |
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462 | (1) |
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34.4 Pairing Correlations |
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463 | (3) |
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466 | (3) |
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Appendix A Coherent-State Path Integral |
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469 | (7) |
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Appendix B Grassman Path Integral |
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476 | (5) |
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Appendix C From Spin Berry Phases to Background Gauge Charges |
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481 | (4) |
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Appendix D Emergent Z2 Gauge Theories |
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485 | (3) |
References |
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488 | (19) |
Index |
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507 | |