Quantum Phase Transitions in Transverse Field Spin Models
From Statistical Physics to Quantum Information

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

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

9781107068797, Cambridge University Press

Hardback, published 28 January 2015

360 pages
24.7 x 18.5 x 2.4 cm, 0.81 kg

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.

List of tables
1. Quantum phase transitions
2. Information theoretic measures close to a quantum critical point
3. Non-equilibrium dynamics across quantum critical points
4. Transverse Ising models in higher dimensions
5. Transverse field models in one dimension
6. Quantum phase transitions in related models
7. Role of quenched disorder
8. Related models with frustration
9. Quantum information theoretic measures: transverse field and related models
10. Non-equilibrium dynamics across quantum critical points: slow quenching
11. Further studies on non-equilibrium dynamics
12. Quenching and quantum information
13. Some very recent developments in information and dynamics
14. Experimental realisations of transverse field Ising systems
15. Adiabatic quantum computations and transverse field models
16. Concluding comments
Appendices
Notes
References
Index.

Subject Areas: Quantum physics [quantum mechanics & quantum field theory PHQ], Physics [PH], Mathematics & science [P]