Quantum Phase Transitions in Transverse Field Spin Models

From Statistical Physics to Quantum Information

Amit Dutta, Gabriel Aeppli, Bikas K. Chakrabarti, Uma Divakaran, Thomas F. Rosenbaum, Diptiman Sen

• Publisher: Cambridge University Press
• Year: 2015
• Print ISBN:
  9781107068797
• eBook ISBN:
  9781316397039
• Topic: Physical Sciences
• Subtopic: Quantum Theory

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.

Table of contents

• Cover
• Title
• Copyright
• Dedication
• Contents
• List of Figures
• List of Tables
• Preface
• Acknowledgements
• I An Introduction to Quantum Phase Transitions, Information and Dynamics
• II Transverse Field Models: Statics
• III Transverse Field and Related Models: Non-Equilibrium Dynamics
• IV Experimental Realizations of Transverse Field Models
• V Quantum Annealing and Adiabatic Quantum Computations Using Transverse Field Models
• Appendix A Derivation of a Matrix Product Hamiltonian
• Appendix B From Jordan–Wigner to Bosonization: Tomonaga–Luttinger Liquids
• Appendix C Calculation of the Entanglement Entropy for a Transverse Ising Chain
• Appendix D The Loschmidt Echo for the One-Dimensional XY Model
• Appendix E Landau–Zener Tunneling: Calculation of Non-Adiabatic Transition Probability
• Appendix F A Note on the Theoretical Studies of Hysteresis
• Bibilography
• Index