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

Author: Amit DuttaGabriel AeppliBikas K ChakrabartiUma DivakaranThomas F RosenbaumAll authors
Publisher: Cambridge : Cambridge University Press, 2015.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book establishes the fundamental connections between the physics of quantum phase transitions and the technological promise of quantum information.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Dutta, Amit.
Quantum Phase Transitions in Transverse Field Spin Models : From Statistical Physics to Quantum Information.
Cambridge : Cambridge University Press, ©2015
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Amit Dutta; Gabriel Aeppli; Bikas K Chakrabarti; Uma Divakaran; Thomas F Rosenbaum; Diptiman Sen
ISBN: 9781316400852 1316400859
OCLC Number: 911000678
Notes: 9.6 Quantum Critical Environment: Decoherence and Loschmidt Echo.
Description: 1 online resource (358 pages)
Contents: Cover; Title; Copyright; Dedication; Contents; List of Figures; List of Tables; Preface; Acknowledgements; I An Introduction to Quantum Phase Transitions, Information and Dynamics; 1 Quantum Phase Transitions; 1.1 Aim and Scope of this Book; 1.2 A Brief Introduction to Classical Phase Transitions: Notion of Universality; 1.3 Quantum Phase Transitions; 1.4 Transverse Ising and XY Models; 1.5 Quantum-Classical Correspondence and Scaling; Path integral formalism; Scaling relations; 1.6 Quantum Rotor Models; 1.7 Josephson Junction Arrays; 1.8 Matrix Product States; 1.9 Chapter Summary. 2 Information Theoretic Measures Close to a Quantum Critical Point2.1 Entanglement Entropy; 2.2 Concurrence; 2.3 Quantum Fidelity; (i) Fidelity susceptibility; (ii) Fidelity per site and fidelity in the thermodynamic limit:; (iii) Multidimensional parameter space; (iv) Other fidelity measures:; 2.4 Chapter Summary; 3 Non-Equilibrium Dynamics across Quantum Critical Points; 3.1 Defect Generation: Kibble-Zurek (KZ) Scaling; 3.2 Adiabatic Perturbation Theory: Slow and Sudden Quenches; Sudden Quenches; 3.3 Thermalization; 3.4 Chapter Summary; II Transverse Field Models: Statics. 4 Transverse Ising Models in Higher Dimensions4.1 Mean Field Theories; (A) Equivalent Single Spin Model; (B) Infinite Range Interactions; (C) Large Spin Limits: Transverse XY Spin Chain; 4.2 Chapter Summary; 5 Transverse Field Models in One Dimension; 5.1 Exact Solution in One Dimension: Jordan-Wigner Transformation; 5.2 Connection to Conformal Field Theory; 5.3 Quantum Spin Chains Coupled to a Bath; 5.4 Chapter Summary; 6 Quantum Phase Transitions in Related Models; 6.1 Some Exactly Solvable Models Related to Transverse Ising and XY Models; 6.2 The Dicke Model. 6.3 Topological Quantum Phase Transitions6.4 Exact Solution of the Kitaev Model; (A) One-Dimensional Model; (B) Two-Dimensional Kitaev Model; 6.5 One-Dimensional p-Wave Superconducting Chain: Majorana Fermions; 6.6 Quantum Phase Transition in Dirac Hamiltonians: Graphene and Topological Insulators; 6.7 Chapter Summary; 7 Role of Quenched Disorder; 7.1 A Modified Harris Criterion; 7.2 Quantum Ising Spin Glass (QISG); 7.3 Griffiths Singularities and Activated Dynamics; 7.4 A Generalized Random Transverse Field Ising Spin Chain. 7.5 Higher Dimensional Realization of Infinite Randomness Fixed Point (IRFP)7.6 Quantum Ising Model in a Random Longitudinal Field; 7.7 Chapter Summary; 8 Related Models with Frustration; 8.1 Quantum ANNNI Model; 8.2 Quantum Lifshitz Point; 8.3 Models with Long-Range Antiferromagnetic Interactions; 8.4 Chapter Summary; 9 Quantum Information Theoretic Measures: Transverse Field and Related Models; 9.1 Concurrence; 9.2 Entanglement Entropy; (i) Pure systems:; (ii) Random systems:; 9.3 Quantum Discord; 9.4 Quantum Fidelity; Other models; 9.5 Scaling of the Geometric Phase Close to a QCP.

Abstract:

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

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