Quantum Phase Transitions in Transverse Field Spin Models

This book establishes the fundamental connections between the physics of quantum phase transitions and the technological promise of quantum information.

This book highlights the problems that remain unresolved and points to future directions of research in non-equilibrium quantum dynamics, quantum information and adiabatic quantum computation using the transverse field and other related models. It should be a valuable resource for a wide audience starting from advanced level undergraduates to researchers.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.