Quantum phase transitions in transverse field spin models: from statistical physics to quantum information
"Discusses the fundamental connections between the physics of quantum phase transitions and the technological promise of quantum information, non-equilibrium quantum dynamics and adiabatic quantum computations"..
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| Format: | Book |
| Language: | English |
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Cambridge
Cambridge University Press
2015
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| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027990497&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027990497&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Summary: | "Discusses the fundamental connections between the physics of quantum phase transitions and the technological promise of quantum information, non-equilibrium quantum dynamics and adiabatic quantum computations".. |
| Physical Description: | XVI, 330 Seiten Illustrationen, Diagramme |
| ISBN: | 9781107068797 |
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| adam_text | This book establishes the fundamental connections between the physics of quantum
phase transitions on the one hand and the technological promise of quantum
information, non-equilibrium quantum dynamics and adiabatic quantum computations
on the other. Starting from the very basics, it features recent theoretical and
experimental results.
The transverse field Ising and XY models (the simplest quantum spin models) provide
the organizing principle for the rich variety of interconnected subjects which are
covered in this book. From a generic introduction to in-depth discussions of the
subtleties of the transverse field Ising and related models, it includes the essentials of
quantum dynamics and quantum information. A wide range of relevant topics has been
discussed: quantum phase transitions, various measures of quantum information, the
effects of disorder and frustration, quenching dynamics and the Kibble-Zurek scaling
relation, the Kitaev model, topological phases of quantum systems, and bosonization. In
addition, it discusses the experimental studies of transverse field models (including the
first experimental realization of quantum annealing) and the recent realization of the
transverse field Ising model using tunable Josephson junctions. Further, it points out
obstacles still remaining in developing a successful quantum computer.
Amit Dutta is Professor of Physics at the Indian Institute of Technology, Kanpur.
Gabriel Aeppli is Professor at the Swiss Federal Institutes of Technology and Head of
Synchrotron Radiation and Nanotechnology at the Paul Scherrer Institute, Switzerland.
Bikas K. Chakrabarti is Prolessor and Director at the Saha Institute of Nuclear Physics,
Kolkata.
Uma Divakaran is DST (India) INSPIRE faculty at the Department of Physics, Indian
Institute of Technology, Kanpur.
Thomas F. Rosenbaum is Professor of Physics and President of the California Institute
of Technology, Pasadena.
Diptiman Sen is Professor at the Centre for High Energy Physics, Indian Institute of
Science, Bangalore.
Contents
List of Figures and Tables ix
Preface xv
Acknowledgements xvii
I An Introduction to Quantum Phase Transitions,
Information and Dynamics 1
1. Quantum Phase Transitions 3
1.1 Aim and Scope of this Book 3
1.2 A Brief Introduction to Classical Phase Transitions: Notion of Universality 12
1.3 Quantum Phase Transitions 14
1.4 Transverse Ising and XY Models 17
1.5 Quantum-Classical Correspondence and Scaling 22
1.6 Quantum Rotor Models 28
1.7 Josephson Junction Arrays 29
1.8 Matrix Product States 30
1.9 Chapter Summary 31
2. Information Theoretic Measures Close to a Quantum Critical Point 32
2.1 Entanglement Entropy 32
2.2 Concurrence 34
2.3 Quantum Fidelity 36
2.4 Chapter Summary 42
3. Non-Equilibrium Dynamics across Quantum Critical Points 44
3.1 Defect Generation: Kibble-Zurek (KZ) Scaling 45
3.2 Adiabatic Perturbation Theory: Slow and Sudden Quenches 49
3.3 Thermalization 53
3.4 Chapter Summary 54
II Transverse Field Models; Statics 57
4. Transverse Ising Models in Higher Dimensions 59
4.1 Mean Field Theories 59
vi Contents
(A) Equivalent Single Spin Model 59
(B) Infinite Range Interactions 60
(C) Large Spin Limits: Transverse XY Spin Chain 62
4.2 Chapter Summary 64
5. Transverse Field Models in One Dimension 65
5.1 Exact Solution in One Dimension: Jordan—Wigner Transformation 65
5.2 Connection to Conformal Field Theory 68
5.3 Quantum Spin Chains Coupled to a Bath 72
5.4 Chapter Summary 74
6. Quantum Phase Transitions in Related Models 75
6.1 Some Exactly Solvable Models Related to Transverse Ising and
XY Models 75
6.2 The Dicke Model 78
6.3 Topological Quantum Phase Transitions 80
6.4 Exact Solution of the Kitaev Model 80
(A) One-Dimensional Model 81
(B) Two-Dimensional Kitaev Model 84
6.5 One-Dimensional p-Wave Superconducting Chain: Majorana Fermions 89
6.6 Quantum Phase Transition in Dirac Hamiltonians: Graphene and
Topological Insulators 93
6.7 Chapter Summary 98
7. Role of Quenched Disorder 100
7.1 A Modified Harris Criterion 100
7.2 Quantum Ising Spin Glass (QISG) 101
7.3 Griffiths Singularities and Activated Dynamics 104
7.4 A Generalized Random Transverse Field Ising Spin Chain 107
7.5 Higher Dimensional Realization of Infinite Randomness Fixed Point
(IRFP) 108
7.6 Quantum Ising Model in a Random Longitudinal Field 110
7.7 Chapter Summary 111
8. Related Models with Frustration 112
8.1 Quantum ANNNI Model 112
8.2 Quantum Lifshitz Point 119
8.3 Models with Long-Range Antiferromagnetic Interactions 120
8.4 Chapter Summary 121
9. Quantum Information Theoretic Measures: Transverse Field and
Related Models 122
Contents vii
9.1 C oncurrence 122
9.2 Entanglement Entropy 124
9.3 Quantum Discord 127
9.4 Quantum Fidelity 129
9.5 Scaling of the Geometric Phase Close to a QCP 133
9.6 Quantum Critical Environment: Decoherence and Loschmidt Echo 135
9.7 Role of Marginality in the Scaling of Fidelity: 2D Dirac Point 139
9.8 Fidelity Susceptibility for a Model with vd 2 144
9.9 Chapter Summary 147
III Transverse Field and Related Models: Non-Equilibrium
Dynamics 149
10. Non-Equilibrium Dynamics Across Quantum Critical Points:
Slow Quenching 151
10.1 Linear and Non-Linear Slow Evolution through Critical Points 151
10.2 Quenching through Multicritical Points 156
10.3 Generalized Quenching Schemes 158
10.4 Quenching through Gapless Phases 161
10.5 Quenching through an Anisotropic Quantum Critical Point 164
10.6 Generalized Kibble-Zurek Scaling Relation 164
10.7 Quenching of a Disordered Chain 166
10.8 Quenching with Coupling to a Bath 167
10.9 KZ Mechanism and Adiabatic Evolution 168
10.10 KZ Mechanism in Space 170
10.11 Chapter Summary 171
11. Further Studies on Non-Equilibrium Dynamics 174
11.1 Sudden Quenches: Defect and Heat Density 174
11.2 Sudden Quenches: Semiclassical Theory 176
11.3 Local Quench 180
11.4 Dynamics Following a Rapid Quenching through a QCP 182
11.5 Effect of Topology on Quantum Quenching 186
11.6 Studies of Tomonaga-Luttinger Liquids 191
11.7 Chapter Summary 192
12. Quenching and Quantum Information 194
12.1 Slow Quenches 194
12.2 Sudden Quenches 200
12.3 Dynamics of Decoherence 202
viii Contents
12.4 Chapter Summary 205
13. Some Recent Developments in Information and Dynamics 207
13.1 Transitionless Dynamics 207
13.2 Quenches, Loschmidt Echo and Nonanalyticities 210
13.3 Periodic Driving and Floquet Theory: Transverse Ising Model 213
13.4 Dynamical Generation of Edge States 216
13.5 Dynamics of a Chain of Hard Core Bosons: Dynamical Localization 220
13.6 Chapter Summary 225
IV Experimental Realizations of Transverse Field Models 229
14. Experimental Realizations of Transverse Field Ising Systems 231
14.1 Singlet Ground State Magnets 231
14.2 Order/Disorder Transitions in Hydrogen-Bonded and Other
Ferro/Antiferroelectric Systems 233
14.3 Low-Dimensional Magnetic Realizations of the Transverse
Field Ising Model 235
14.4 Ising Doublets in External Magnetic Fields in Three-Dimensions 237
14.5 Disorder and the Transverse Field Ising Model 239
14.6 Chapter Summary 244
V Quantum Annealing and Adiabatic Quantum Computations
Using Transverse Field Models 245
15. Adiabatic Quantum Computations and Transverse Field Models 247
15.1 Theoretical Studies 249
15.2 Experimental Studies 254
15.3 A Quantum Computer in the Making? 261
15.4 Chapter Summary 263
16. Concluding Comments 265
Appendix A Derivation of a Matrix Product Hamiltonian 267
Appendix B From Jordan—Wigner to Bosonization: Tomonaga-Luttinger Liquids 269
Appendix C Calculation of the Entanglement Entropy for a Transverse Ising Chain 278
Appendix D The Loschmidt Echo for the One-Dimensional XY Model 281
Appendix E Landau—Zener Tunneling: Calculation of Non-Adiabatic Transition
Probability 283
Appendix F A Note on the Theoretical Studies of Hysteresis 292
Bibliography 295
Index 329
Color Plates 331
|
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| indexdate | 2024-12-20T17:14:17Z |
| institution | BVB |
| isbn | 9781107068797 |
| language | English |
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| spellingShingle | Dutta, Amit 1968- Quantum phase transitions in transverse field spin models from statistical physics to quantum information Phase transformations (Statistical physics) Phase rule and equilibrium Spinmodell (DE-588)4272227-5 gnd Quantenphasenübergang (DE-588)4793582-0 gnd Quanteninformatik (DE-588)4705961-8 gnd |
| subject_GND | (DE-588)4272227-5 (DE-588)4793582-0 (DE-588)4705961-8 |
| title | Quantum phase transitions in transverse field spin models from statistical physics to quantum information |
| title_auth | Quantum phase transitions in transverse field spin models from statistical physics to quantum information |
| title_exact_search | Quantum phase transitions in transverse field spin models from statistical physics to quantum information |
| title_full | Quantum phase transitions in transverse field spin models from statistical physics to quantum information Amit Dutta [und 5 weitere] |
| title_fullStr | Quantum phase transitions in transverse field spin models from statistical physics to quantum information Amit Dutta [und 5 weitere] |
| title_full_unstemmed | Quantum phase transitions in transverse field spin models from statistical physics to quantum information Amit Dutta [und 5 weitere] |
| title_short | Quantum phase transitions in transverse field spin models |
| title_sort | quantum phase transitions in transverse field spin models from statistical physics to quantum information |
| title_sub | from statistical physics to quantum information |
| topic | Phase transformations (Statistical physics) Phase rule and equilibrium Spinmodell (DE-588)4272227-5 gnd Quantenphasenübergang (DE-588)4793582-0 gnd Quanteninformatik (DE-588)4705961-8 gnd |
| topic_facet | Phase transformations (Statistical physics) Phase rule and equilibrium Spinmodell Quantenphasenübergang Quanteninformatik |
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