Quantum Phase Transitions in Transverse Field Models

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Cambridge University Press, Jan 28, 2015 - Science - 330 pages
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 Kibble-Zurek 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.
 

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Contents

Information Theoretic Measures Close to a Quantum Critical Point
32
NonEquilibrium Dynamics across Quantum Critical Points
44
Transverse Ising Models in Higher Dimensions
59
Transverse Field Models in One Dimension
65
Quantum Phase Transitions in Related Models
75
Role of Quenched Disorder
100
Related Models with Frustration
112
Transverse Field
122
Further Studies on NonEquilibrium Dynamics
174
Quenching and Quantum Information
194
Experimental Realizations of Transverse Field Ising Systems
231
Quantum Annealing and Adiabatic Quantum Computations
245
Concluding Comments
265
Calculation of the Entanglement Entropy for a Transverse Ising Chain
278
Appendix F A Note on the Theoretical Studies of Hysteresis
292
Index
329

NonEquilibrium
149

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About the author (2015)

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.

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.

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