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Quantum Phase Transitions in Transverse Field Spin Models: From Statistical Physics to Quantum Information [Kietas viršelis]

(Indian Institute of Technology, Kanpur), (Indian Institute of Science, Bangalore), (University College London), (Saha Institute of Nuclear Physics, India), (Indian Institute of Technology, Kanpur), (University of Chicago)
  • Formatas: Hardback, 360 pages, aukštis x plotis x storis: 247x185x24 mm, weight: 820 g
  • Išleidimo metai: 28-Jan-2015
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107068797
  • ISBN-13: 9781107068797
Kitos knygos pagal šią temą:
  • Formatas: Hardback, 360 pages, aukštis x plotis x storis: 247x185x24 mm, weight: 820 g
  • Išleidimo metai: 28-Jan-2015
  • Leidėjas: Cambridge University Press
  • ISBN-10: 1107068797
  • ISBN-13: 9781107068797
Kitos knygos pagal šią temą:
The transverse field Ising and XY models (the simplest quantum spin models) provide the organising 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 also been provided: quantum phase transitions, various measures of quantum information, the effects of disorder and frustration, quenching dynamics and the KibbleZurek scaling relation, the Kitaev model, topological phases of quantum systems, and bosonisation. In addition, it also discusses the experimental studies of transverse field models (including the first experimental realisation of quantum annealing) and the recent realisation of the transverse field Ising model using tunable Josephson junctions. Further, it points to the obstacles still remaining to develop a successful quantum computer.

Daugiau informacijos

This book establishes the fundamental connections between the physics of quantum phase transitions and the technological promise of quantum information.
List of Figures and Tables ix
Preface xv
Acknowledgements xvii
I An Introduction to Quantum Phase Transitions, Information and Dynamics 1(56)
1 Quantum Phase Transitions
3(29)
1.1 Aim and Scope of this Book
3(9)
1.2 A Brief Introduction to Classical Phase Transitions: Notion of Universality
12(2)
1.3 Quantum Phase Transitions
14(3)
1.4 Transverse Ising and XY Models
17(5)
1.5 Quantum-Classical Correspondence and Scaling
22(6)
1.6 Quantum Rotor Models
28(1)
1.7 Josephson Junction Arrays
29(1)
1.8 Matrix Product States
30(1)
1.9
Chapter Summary
31(1)
2 Information Theoretic Measures Close to a Quantum Critical Point
32(12)
2.1 Entanglement Entropy
32(2)
2.2 Concurrence
34(2)
2.3 Quantum Fidelity
36(6)
2.4
Chapter Summary
42(2)
3 Non-Equilibrium Dynamics across Quantum Critical Points
44(13)
3.1 Defect Generation: Kibble—Zurek (KZ) Scaling
45(4)
3.2 Adiabatic Perturbation Theory: Slow and Sudden Quenches
49(4)
3.3 Thermalization
53(1)
3.4
Chapter Summary
54(3)
II Transverse Field Models: Statics 57(92)
4 Transverse Ising Models in Higher Dimensions
59(6)
4.1 Mean Field Theories
59(5)
A Equivalent Single Spin Model
59(1)
B Infinite Range Interactions
60(2)
C Large Spin Limits: Transverse XY Spin Chain
62(2)
4.2
Chapter Summary
64(1)
5 Transverse Field Models in One Dimension
65(10)
5.1 Exact Solution in One Dimension: Jordan—Wigner Transformation
65(3)
5.2 Connection to Conformal Field Theory
68(4)
5.3 Quantum Spin Chains Coupled to a Bath
72(2)
5.4
Chapter Summary
74(1)
6 Quantum Phase Transitions in Related Models
75(25)
6.1 Some Exactly Solvable Models Related to Transverse Ising and XY Models
75(3)
6.2 The Dicke Model
78(2)
6.3 Topological Quantum Phase Transitions
80(1)
6.4 Exact Solution of the Kitaev Model
80(9)
A One-Dimensional Model
81(3)
B Two-Dimensional Kitaev Model
84(5)
6.5 One-Dimensional p-Wave Superconducting Chain: Majorana Fermions
89(4)
6.6 Quantum Phase Transition in Dirac Hamiltonian: Graphene and Topological Insulators
93(5)
6.7
Chapter Summary
98(2)
7 Role of Quenched Disorder
100(12)
7.1 A Modified Harris Criterion
100(1)
7.2 Quantum Ising Spin Glass (QISG)
101(3)
7.3 Griffiths Singularities and Activated Dynamics
104(3)
7.4 A Generalized Random Transverse Field Ising Spin Chain
107(1)
7.5 Higher Dimensional Realization of Infinite Randomness Fixed Point (IRFP)
108(2)
7.6 Quantum Ising Model in a Random Longitudinal Field
110(1)
7.7
Chapter Summary
111(1)
8 Related Models with Frustration
112(10)
8.1 Quantum ANNNI Model
112(7)
8.2 Quantum Lifshitz Point
119(1)
8.3 Models with Long-Range Antiferromagnetic Interactions
120(1)
8.4
Chapter Summary
121(1)
9 Quantum Information Theoretic Measures: Transverse Field and Related Models
122(27)
9.1 Concurrence
122(2)
9.2 Entanglement Entropy
124(3)
9.3 Quantum Discord
127(2)
9.4 Quantum Fidelity
129(4)
9.5 Scaling of the Geometric Phase Close to a QCP
133(2)
9.6 Quantum Critical Environment: Decoherence and Loschmidt Echo
135(4)
9.7 Role of Marginality in the Scaling of Fidelity: 2D Dirac Point
139(5)
9.8 Fidelity Susceptibility for a Model with vd > 2
144(3)
9.9
Chapter Summary
147(2)
III Transverse Field and Related Models: Non-Equilibrium Dynamics 149(80)
10 Non-Equilibrium Dynamics Across Quantum Critical Points: Slow Quenching
151(23)
10.1 Linear and Non-Linear Slow Evolution through Critical Points
151(5)
10.2 Quenching through Multicritical Points
156(2)
10.3 Generalized Quenching Schemes
158(3)
10.4 Quenching through Gapless Phases
161(3)
10.5 Quenching through an Anisotropic Quantum Critical Point
164(1)
10.6 Generalized Kibble-Zurek Scaling Relation
164(2)
10.7 Quenching of a Disordered Chain
166(1)
10.8 Quenching with Coupling to a Bath
167(1)
10.9 KZ Mechanism and Adiabatic Evolution
168(2)
10.10 KZ Mechanism in Space
170(1)
10.11
Chapter Summary
171(3)
11 Further Studies on Non-Equilibrium Dynamics
174(20)
11.1 Sudden Quenches: Defect and Heat Density
174(2)
11.2 Sudden Quenches: Semiclassical Theory
176(4)
11.3 Local Quench
180(2)
11.4 Dynamics Following a Rapid Quenching through a QCP
182(4)
11.5 Effect of Topology on Quantum Quenching
186(5)
11.6 Studies of Tomonaga-Luttinger Liquids
191(1)
11.7
Chapter Summary
192(2)
12 Quenching and Quantum Information
194(13)
12.1 Slow Quenches
194(6)
12.2 Sudden Quenches
200(2)
12.3 Dynamics of Decoherence
202(3)
12.4
Chapter Summary
205(2)
13 Some Recent Developments in Information and Dynamics
207(22)
13.1 Transitionless Dynamics
207(3)
13.2 Quenches, Loschmidt Echo and Nonanalyticities
210(3)
13.3 Periodic Driving and Floquet Theory: Transverse Ising Model
213(3)
13.4 Dynamical Generation of Edge States
216(4)
13.5 Dynamics of a Chain of Hard Core Bosons: Dynamical Localization
220(5)
13.6
Chapter Summary
225(4)
IV Experimental Realizations of Transverse Field Models 229(16)
14 Experimental Realizations of Transverse Field Ising Systems
231(14)
14.1 Singlet Ground State Magnets
231(2)
14.2 Order/Disorder Transitions in Hydrogen-Bonded and Other Ferro/Antiferroelectric Systems
233(2)
14.3 Low-Dimensional Magnetic Realizations of the Transverse Field Ising Model
235(2)
14.4 Ising Doublets in External Magnetic Fields in Three-Dimensions
237(2)
14.5 Disorder and the Transverse Field Ising Model
239(5)
14.6
Chapter Summary
244(1)
V Quantum Annealing and Adiabatic Quantum Computations Using Transverse Field Models 245(22)
15 Adiabatic Quantum Computations and Transverse Field Models
247(18)
15.1 Theoretical Studies
249(5)
15.2 Experimental Studies
254(7)
15.3 A Quantum Computer in the Making?
261(2)
15.4
Chapter Summary
263(2)
16 Concluding Comments
265(2)
Appendix A Derivation of a Matrix Product Hamiltonian 267(2)
Appendix B From Jordan—Wigner to Bosonization: Tomonaga—Luttinger Liquids 269(9)
Appendix C Calculation of the Entanglement Entropy for a Transverse Ising Chain 278(3)
Appendix D The Loschmidt Echo for the One-Dimensional XY Model 281(2)
Appendix E Landau—Zener Tunneling: Calculation of Non-Adiabatic Transition Probability 283(9)
Appendix F A Note on the Theoretical Studies of Hysteresis 292(3)
Bibliography 295(34)
Index 329(2)
Color Plates 331
Amit Dutta holds a PhD from the Saha Institute of Nuclear Physics, Kolkata. After postdoctoral experience at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, and at Wuerzburg University, Germany, he joined the Indian Institute of Technology, Kanpur, in 2003, where he is currently a professor. He has written several highly cited papers on quantum phase transitions, quantum non-equilibrium dynamics and quantum information, and coauthored Quantum Ising Phases and Transitions in Transverse Ising Models (1996). He is a regular associate of the Abdus Salam International Center for Theoretical Physics, Trieste, Italy. Gabriel Aeppli is Quain Professor of Physics and Director at the London Centre for Nanotechnology. Prior to taking up these positions in the autumn of 2002, he was a Senior Research Scientist for NEC (Princeton), a Distinguished Member of Technical Staff at Bell Laboratories, a Research Assistant at the Massachusetts Institute of Technology, and an industrial co-op student at IBM. He holds a BSc in Mathematics and a PhD from the Massachusetts Institute of Technology. His honours include Fellowship of the Royal Society (2010), the IOP (Institute of Physics) Mott Prize (2008), the APS Oliver Buckley Prize (2005), the IUPAP Magnetism Prize/Neel Medal (2003), a Riso National Laboratory Fellowship (2002), the Royal Society Wolfson Research Merit Award (2002), the post of Mildner Lecturer at the Department of Electronic and Electrical Engineering, University College London (2002), Fellowship of the American Physical Society (1997) and Fellowship of the Japan Society for the Promotion of Science (1996). In addition, he has been a member and chairman of many panels, sponsored by the USDOE, the American Physical Society, EPSRC, and the National Research Council (US), among others. His personal research is currently focused on quantum information processing, magnetism, superconductivity, and the implications of nanotechnology for information processing and health care. Bikas K. Chakrabarti is Senior Professor of Theoretical Condensed Matter Physics at the Saha Institute of Nuclear Physics, Kolkata, and Visiting Professor of Economics at the Indian Statistical Institute, Kolkata. He received his doctorate in physics from Calcutta University in 1979. Following postdoctoral positions at the University of Oxford and Cologne University, he joined SINP in 1983. His research interests include the physics of fracture, quantum glasses, and the interdisciplinary sciences of optimisation, brain modelling, and econophysics. He has written several books and reviews on these topics. Professor Chakrabarti is a recipient of the S. S. Bhatnagar Award (1997). He has also received the Outstanding Referee Award of the American Physical Society (2010). Uma Divakaran holds Masters and PhD degrees from the Indian Institute of Technology, Kanpur. She is a recipient of the Alexander von Humboldt Postdoctoral Fellowship (2010) and worked in the group of Professor Heiko Rieger at Saarland University, Germany. She was also a Junior Associate of the Abdus Salam International Center for Theoretical Physics, Trieste, Italy, from 2009 to 2014. She is presently a Postdoctoral Fellow at the Indian Institute of Technology, Kanpur. She has worked on non-equilibrium dynamics and has written several highly cited papers on these topics. Thomas F. Rosenbaum holds a bachelor's degree in Physics with honors from Harvard University, and an MA and PhD in Physics from Princeton University. He presently serves as Provost of the University of Chicago. In addition to his responsibilities for academic and research programmes across the University, Rosenbaum serves on the Board of Governors for Argonne National Laboratory. He is an expert on the quantum mechanical nature of materials the physics of electronic, magnetic and optical materials at the atomic level that are best observed at temperatures near absolute zero. He conducted research at Bell Laboratories and at IBM Watson Research Center before joining the Chicago faculty in 1983. He directed the University's Materials Research Laboratory from 1991 to 1994 and the University's James Franck Institute from 1995 to 2001, and served as Vice President for Research and for Argonne National Laboratory from 2002 to 2006. His honours include an Alfred P. Sloan Research Fellowship, a Presidential Young Investigator Award, and the William McMillan Award for Outstanding Contributions to Condensed Matter Physics. Rosenbaum is an elected fellow and Centennial Lecturer of the American Physical Society, and an elected fellow of the American Academy of Arts and Sciences and the American Association for the Advancement of Science. He is also a member of the Board of Directors of the Bulletin of the Atomic Scientists. Diptiman Sen received his PhD in Physics from Princeton University in 1984. After postdoctoral work at Carnegie Mellon University and the University of Edinburgh, he joined the Indian Institute of Science in 1988 where he is now a Professor. His research interests include condensed matter systems in low dimensions, mesoscopic systems, and various aspects of quantum field theory. He is a member of the Editorial Board of Physical Review Letters for the period 2009 to 2015, and was recognised by the American Physical Society as an Outstanding Referee in 2009.