List of Figures and Tables |
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ix | |
Preface |
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xv | |
Acknowledgements |
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xvii | |
I An Introduction to Quantum Phase Transitions, Information and Dynamics |
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1 | (56) |
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1 Quantum Phase Transitions |
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3 | (29) |
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1.1 Aim and Scope of this Book |
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3 | (9) |
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1.2 A Brief Introduction to Classical Phase Transitions: Notion of Universality |
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12 | (2) |
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1.3 Quantum Phase Transitions |
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14 | (3) |
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1.4 Transverse Ising and XY Models |
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17 | (5) |
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1.5 Quantum-Classical Correspondence and Scaling |
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22 | (6) |
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28 | (1) |
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1.7 Josephson Junction Arrays |
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29 | (1) |
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1.8 Matrix Product States |
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30 | (1) |
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31 | (1) |
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2 Information Theoretic Measures Close to a Quantum Critical Point |
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32 | (12) |
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32 | (2) |
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34 | (2) |
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36 | (6) |
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42 | (2) |
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3 Non-Equilibrium Dynamics across Quantum Critical Points |
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44 | (13) |
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3.1 Defect Generation: KibbleZurek (KZ) Scaling |
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45 | (4) |
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3.2 Adiabatic Perturbation Theory: Slow and Sudden Quenches |
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49 | (4) |
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53 | (1) |
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54 | (3) |
II Transverse Field Models: Statics |
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57 | (92) |
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4 Transverse Ising Models in Higher Dimensions |
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59 | (6) |
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59 | (5) |
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A Equivalent Single Spin Model |
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59 | (1) |
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B Infinite Range Interactions |
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60 | (2) |
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C Large Spin Limits: Transverse XY Spin Chain |
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62 | (2) |
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64 | (1) |
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5 Transverse Field Models in One Dimension |
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65 | (10) |
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5.1 Exact Solution in One Dimension: JordanWigner Transformation |
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65 | (3) |
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5.2 Connection to Conformal Field Theory |
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68 | (4) |
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5.3 Quantum Spin Chains Coupled to a Bath |
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72 | (2) |
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74 | (1) |
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6 Quantum Phase Transitions in Related Models |
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75 | (25) |
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6.1 Some Exactly Solvable Models Related to Transverse Ising and XY Models |
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75 | (3) |
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78 | (2) |
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6.3 Topological Quantum Phase Transitions |
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80 | (1) |
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6.4 Exact Solution of the Kitaev Model |
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80 | (9) |
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81 | (3) |
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B Two-Dimensional Kitaev Model |
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84 | (5) |
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6.5 One-Dimensional p-Wave Superconducting Chain: Majorana Fermions |
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89 | (4) |
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6.6 Quantum Phase Transition in Dirac Hamiltonian: Graphene and Topological Insulators |
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93 | (5) |
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98 | (2) |
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7 Role of Quenched Disorder |
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100 | (12) |
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7.1 A Modified Harris Criterion |
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100 | (1) |
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7.2 Quantum Ising Spin Glass (QISG) |
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101 | (3) |
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7.3 Griffiths Singularities and Activated Dynamics |
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104 | (3) |
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7.4 A Generalized Random Transverse Field Ising Spin Chain |
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107 | (1) |
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7.5 Higher Dimensional Realization of Infinite Randomness Fixed Point (IRFP) |
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108 | (2) |
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7.6 Quantum Ising Model in a Random Longitudinal Field |
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110 | (1) |
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111 | (1) |
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8 Related Models with Frustration |
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112 | (10) |
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112 | (7) |
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8.2 Quantum Lifshitz Point |
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119 | (1) |
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8.3 Models with Long-Range Antiferromagnetic Interactions |
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120 | (1) |
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121 | (1) |
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9 Quantum Information Theoretic Measures: Transverse Field and Related Models |
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122 | (27) |
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122 | (2) |
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124 | (3) |
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127 | (2) |
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129 | (4) |
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9.5 Scaling of the Geometric Phase Close to a QCP |
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133 | (2) |
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9.6 Quantum Critical Environment: Decoherence and Loschmidt Echo |
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135 | (4) |
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9.7 Role of Marginality in the Scaling of Fidelity: 2D Dirac Point |
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139 | (5) |
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9.8 Fidelity Susceptibility for a Model with vd > 2 |
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144 | (3) |
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147 | (2) |
III Transverse Field and Related Models: Non-Equilibrium Dynamics |
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149 | (80) |
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10 Non-Equilibrium Dynamics Across Quantum Critical Points: Slow Quenching |
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151 | (23) |
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10.1 Linear and Non-Linear Slow Evolution through Critical Points |
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151 | (5) |
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10.2 Quenching through Multicritical Points |
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156 | (2) |
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10.3 Generalized Quenching Schemes |
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158 | (3) |
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10.4 Quenching through Gapless Phases |
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161 | (3) |
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10.5 Quenching through an Anisotropic Quantum Critical Point |
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164 | (1) |
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10.6 Generalized Kibble-Zurek Scaling Relation |
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164 | (2) |
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10.7 Quenching of a Disordered Chain |
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166 | (1) |
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10.8 Quenching with Coupling to a Bath |
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167 | (1) |
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10.9 KZ Mechanism and Adiabatic Evolution |
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168 | (2) |
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10.10 KZ Mechanism in Space |
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170 | (1) |
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171 | (3) |
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11 Further Studies on Non-Equilibrium Dynamics |
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174 | (20) |
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11.1 Sudden Quenches: Defect and Heat Density |
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174 | (2) |
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11.2 Sudden Quenches: Semiclassical Theory |
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176 | (4) |
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180 | (2) |
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11.4 Dynamics Following a Rapid Quenching through a QCP |
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182 | (4) |
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11.5 Effect of Topology on Quantum Quenching |
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186 | (5) |
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11.6 Studies of Tomonaga-Luttinger Liquids |
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191 | (1) |
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192 | (2) |
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12 Quenching and Quantum Information |
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194 | (13) |
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194 | (6) |
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200 | (2) |
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12.3 Dynamics of Decoherence |
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202 | (3) |
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205 | (2) |
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13 Some Recent Developments in Information and Dynamics |
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207 | (22) |
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13.1 Transitionless Dynamics |
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207 | (3) |
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13.2 Quenches, Loschmidt Echo and Nonanalyticities |
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210 | (3) |
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13.3 Periodic Driving and Floquet Theory: Transverse Ising Model |
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213 | (3) |
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13.4 Dynamical Generation of Edge States |
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216 | (4) |
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13.5 Dynamics of a Chain of Hard Core Bosons: Dynamical Localization |
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220 | (5) |
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225 | (4) |
IV Experimental Realizations of Transverse Field Models |
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229 | (16) |
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14 Experimental Realizations of Transverse Field Ising Systems |
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231 | (14) |
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14.1 Singlet Ground State Magnets |
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231 | (2) |
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14.2 Order/Disorder Transitions in Hydrogen-Bonded and Other Ferro/Antiferroelectric Systems |
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233 | (2) |
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14.3 Low-Dimensional Magnetic Realizations of the Transverse Field Ising Model |
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235 | (2) |
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14.4 Ising Doublets in External Magnetic Fields in Three-Dimensions |
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237 | (2) |
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14.5 Disorder and the Transverse Field Ising Model |
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239 | (5) |
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244 | (1) |
V Quantum Annealing and Adiabatic Quantum Computations Using Transverse Field Models |
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245 | (22) |
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15 Adiabatic Quantum Computations and Transverse Field Models |
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247 | (18) |
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249 | (5) |
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15.2 Experimental Studies |
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254 | (7) |
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15.3 A Quantum Computer in the Making? |
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261 | (2) |
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263 | (2) |
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265 | (2) |
Appendix A Derivation of a Matrix Product Hamiltonian |
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267 | (2) |
Appendix B From JordanWigner to Bosonization: TomonagaLuttinger Liquids |
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269 | (9) |
Appendix C Calculation of the Entanglement Entropy for a Transverse Ising Chain |
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278 | (3) |
Appendix D The Loschmidt Echo for the One-Dimensional XY Model |
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281 | (2) |
Appendix E LandauZener Tunneling: Calculation of Non-Adiabatic Transition Probability |
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283 | (9) |
Appendix F A Note on the Theoretical Studies of Hysteresis |
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292 | (3) |
Bibliography |
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295 | (34) |
Index |
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329 | (2) |
Color Plates |
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331 | |