Kooperativer Bibliotheksverbund

UID:

Format: XVI, 541 p. 148 illus., 141 illus. in color. , online resource.

Edition: 1st ed. 2022.

ISBN: 9783031039980

Series Statement: Quantum Science and Technology,

Content: This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.

Note: Chapter 1: Entanglement spectra of spin chains -- Chapter 2: Detecting quantum phase transitions in spin chains -- Chapter 3: Entanglement entropy in critical quantum spin chains with boundaries and defects -- Chapter 4: Entanglement entropy and localization in disordered quantum chains -- Chapter 5: Some aspects of Aeck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation -- Chapter 6: Machine-learning-assisted entanglement -- Chapter 7: Local Convertibility in quantum spin -- Chapter 8: Optimal parent Hamiltonians for many-body -- Chapter 9: Entanglement dynamics in hybrid quantum circuits -- Chapter 10: Quantum simulation using noisy unitary circuits and measurements -- Chapter 12: Quantum map approach to entanglement -- Chapter 13: Weak ergodicity breaking through the lens of quantum entanglement -- Chapter 14: Quench dynamics of Rényi negativities -- Chapter 15: Phases and dynamics of ultracold bosons in a tilted optical lattice -- Chapter 16: NMR experimental study of out-of-equilibrium -- Chapter 17: Quantum-dot spin chains.

In: Springer Nature eBook

Additional Edition: Printed edition: ISBN 9783031039973

Additional Edition: Printed edition: ISBN 9783031039997

Additional Edition: Printed edition: ISBN 9783031040009

Language: English

DOI: 10.1007/978-3-031-03998-0

URL: https://doi.org/10.1007/978-3-031-03998-0

URL: Volltext  (URL des Erstveröffentlichers)

UID:

Format: 1 online resource (549 pages)

ISBN: 3-031-03998-X

Series Statement: Quantum Science and Technology

Note: Includes index. , Intro -- Preface -- References -- Contents -- Editors and Contributors -- About the Editors -- Contributors -- Entanglement Spectra of Spin Chains -- 1 Entanglement Spectra of Many-Body Ground States -- 2 Decomposition of Spin Chain Hilbert Spaces -- 3 Gapped Spin Chains -- 4 Gapless Spin Chains -- 5 Conclusion -- References -- Detecting Quantum Phase Transitions in Spin Chains -- 1 Introduction to Quantum Entanglement -- 1.1 Quantum Entanglement and Quantum Phase Transitions -- 1.2 Methodologies from the Viewpoint of Quantum Information Theory -- 1.3 Open Questions -- 2 Concurrence and Quantum Phase Transitions in Spin Chains -- 3 von Neumann Entropy and Quantum Phase Transitions -- 3.1 Single-Site Entanglement -- 3.2 Multisite Entanglement -- 3.3 Entanglement and Quantum Phase Transitions at Finite Temperatures -- 3.4 Entanglement and Quantum Correlations -- 4 Quantum Discord, Quantum Coherence, and Quantum Phase Transitions -- 4.1 Quantum Discord -- 4.2 Quantum Coherence and Quantum Coherence Spectrum -- 5 Deducing Order Parameters from Entanglement Based Method -- 6 Summary and Outlook -- References -- Entanglement Entropy in Critical Quantum Spin Chains with Boundaries and Defects -- 1 Introduction -- 2 Entanglement Entropy in CFTs with Boundaries -- 2.1 Ising Model -- 2.2 The Free, Compactified Boson Model -- 3 Entanglement Entropy in CFTs with Defects -- 3.1 The Ising Model -- 3.1.1 Energy Defect -- 3.1.2 Duality Defect -- 3.2 The Free, Compactified Boson Model -- 4 Conclusion -- References -- Entanglement Entropy and Localization in Disordered QuantumChains -- 1 Introduction -- 1.1 Generalities -- 1.2 Random Spin Chain Models -- 1.2.1 Disordered XXZ Hamiltonians -- 1.2.2 Random Transverse Field Ising Chains -- 1.2.3 Many-Body Localization -- 1.3 Chapter Organization -- 2 Entanglement in Non-interacting Anderson Localized Chains. , 2.1 Disordered XX Chains and Single-Particle Localization Lengths -- 2.1.1 Localization Length from the Participation Ratio (PR) -- 2.1.2 Numerical Results for the Localization Lengths -- 2.2 Entanglement Entropy for Many-Body (Anderson Localized) Eigenstates -- 2.2.1 Free-Fermion Entanglement Entropy -- 2.2.2 Low and High Energy -- 2.2.3 Strong Disorder Limit -- 3 Entanglement and Infinite Randomness Criticalities -- 3.1 Entanglement in Disordered XXZ and Quantum Ising Chains -- 3.1.1 Random Singlet State for Disordered S=1/2 Chains -- 3.1.2 Infinite Randomness Criticality at High Energy -- 3.2 Other Systems Showing Infinite Randomness Criticality -- 3.2.1 Higher Spins, Golden Chain, and RG Flows -- 3.2.2 d> -- 1 Infinite Randomness -- 3.3 Engineered Disorders -- 4 Many-Body Localization Probed by Quantum Entanglement -- 4.1 Area vs. Volume-Law Entanglement for High-Energy Eigenstates -- 4.2 Distributions of Entanglement Entropies -- 4.2.1 Distribution Across the ETH-MBL Transition -- 4.2.2 Strong Disorder Distributions -- 5 Concluding Remarks -- References -- Some Aspects of Affleck-Kennedy-Lieb-Tasaki Models: Tensor Network, Physical Properties, Spectral Gap, Deformation, and Quantum Computation -- 1 Introduction -- 2 Tensor-Network Picture: MPS and PEPS -- 2.1 1D AKLT Chain -- 2.2 Two Dimensions -- 2.2.1 Honeycomb/Hexagonal Lattice -- 2.2.2 Square Lattice -- 2.3 Boundary Conditions and Degeneracy of AKLT Models -- 3 Magnetic Ordering -- 4 Symmetry-Protected Topological Order -- 4.1 SPT Order of 1D AKLT State -- 4.2 Two Dimensions: Honeycomb and Square Lattices -- 5 Hidden Order in AKLT States -- 5.1 String Order Parameter -- 5.2 Hidden Cluster Order -- 5.3 Hidden Frustration on Frustrated Lattices -- 6 Applications in Quantum Computation -- 6.1 One Dimension -- 6.1.1 Logical Identity and One-Qubit Gates. , 6.1.2 Reduction to the 1D Cluster State -- 6.2 Two Dimensions: Universal Computation -- 7 Spectral Gap for AKLT Models -- 8 Deformed AKLT Models and Phase Transitions -- 8.1 1D Deformed AKLT Chain -- 8.2 2D Deformed AKLT Models and Their Phase Transitions -- 9 Conclusion -- References -- Machine Learning-Assisted Entanglement Measurement in Quantum Many-Body Systems -- 1 Introduction -- 2 PPT Criterion and Entanglement Measurement -- 2.1 Werner States -- 3 Measuring the PT Moments -- 3.1 Measurement in Spin Systems -- 3.2 Measurement in Bosonic Systems -- 4 Neural Network Entanglement Estimator -- 4.1 Choice of the Training Set -- 4.2 Sensitivity and Error Analysis -- 4.3 Comparison with Approximate State Reconstruction Methods -- 5 Numerical Results -- 5.1 Ground States Through a Quantum Phase Transition -- 5.2 Quench Across a Phase Transition -- 5.3 W-State -- 6 Conclusions -- References -- Local Convertibility in Quantum Spin Systems -- 1 The Cluster-Ising Model -- 2 The λ-D Model -- 3 The Perturbed Toric Code -- 4 The Quantum Ising Chain -- 4.1 The Rényi Entropies -- 4.2 The Correlation Matrix -- 4.3 The Z2 Symmetric Ground State -- 4.4 Symmetry Broken Ground State -- 5 Origin of SSB -- 5.1 Two-Body Quantum Correlations -- 5.2 Global Properties: Local Convertibility and Many-Body Entanglement Sharing -- 5.3 Many-Body Entanglement Distribution -- 6 Conclusions -- Bibliography -- Optimal Parent Hamiltonians for Many-Body States -- 1 Introduction -- 2 The Space of Symmetries -- 3 From Ground States to Parent Hamiltonians -- 4 The Time-Dependent Inverse Problem -- 5 Conclusions -- References -- Entanglement Dynamics in Hybrid Quantum Circuits -- 1 Introduction -- 2 Random Unitary Quantum Circuits -- 2.1 Entanglement Growth -- 2.1.1 Mapping to KPZ Dynamics of Random Surface Growth -- 2.1.2 Directed Polymer and Minimal-Cut Interpretation. , 2.2 Operator Spreading -- 2.3 U(1) Symmetric Circuits -- 3 Measurement-Induced Phase Transitions -- 3.1 Entanglement Transition -- 3.2 Alternative Perspectives on MIPTs -- 3.2.1 Purification Transition -- 3.2.2 Ancilla Probe of Purification Transition -- 3.2.3 Experimental Observation of MIPT in Trapped Ions -- 3.2.4 Connection to Quantum Channel Capacity and Quantum Error Correction -- 3.2.5 Information Gained by the Observer -- 4 Replica Statistical Mechanics Models -- 4.1 Replica Trick -- 4.2 Haar Calculus and Boltzmann Weights -- 4.3 Boundary Conditions and Domain Wall Free Energy -- 4.4 Symmetry and Conformal Invariance -- 4.5 Large Hilbert Space Dimension Limit -- 4.5.1 Mapping Onto Classical Percolation -- 4.5.2 Entanglement and Minimal-Cut Picture -- 4.6 Finite d Universality Class -- 5 Symmetry and Topology in Measurement-Induced Phases and Criticality -- 5.1 Symmetric Monitored Random Circuits -- 5.2 Area-Law Phases -- 5.2.1 Measurement-Induced Symmetry-Breaking Order in 1+1d -- 5.2.2 Measurement-Induced Topological Orders -- 5.3 Volume-Law Phases -- 5.3.1 Volume-Law Phases with Order-Stat-Mech Perspective -- 5.3.2 Charge Sharpening Transitions in the Volume-Law Phase -- 6 Discussion -- References -- Quantum Simulation Using Noisy Unitary Circuits and Measurements -- 1 Introduction -- 2 Measurement-Induced Entanglement Transitions in Hybrid Quantum Circuits -- 2.1 Quantum Trajectories -- 2.2 Monitored Quantum Circuits -- 2.3 Purification Transition -- 2.4 Transitions in the Rényi Entropies -- 2.5 Analytically Tractable Limits -- 2.6 Critical Properties of Measurement-Induced Transitions -- 2.7 Entanglement Transitions in Experiments -- 2.7.1 Scalability Issues -- 2.7.2 Measurement-Induced Transition in a Trapped-Ion Experiment -- 3 Random Circuits on Noisy-Intermediate Scale Quantum Devices. , 3.1 Random-Circuit Sampling for Achieving a Quantum Computational Advantage -- 3.2 Applications of Random Circuits in Quantum Many-Body Physics -- 4 Conclusion -- References -- Entanglement Dynamics in Spin Chains with Structured Long-Range Interactions -- 1 Introduction -- 2 Quantifying Entanglement and Information Spreading -- 2.1 Measures of Entanglement Entropy -- 2.2 Lieb-Robinson Bounds and OTOCs -- 2.3 Quasiparticle Approaches -- 2.4 Matrix Product States (MPS) -- 3 Power-Law Interacting Models -- 3.1 Short-Range Regime, α> -- 2 -- 3.2 Intermediate Range Regime, 1 < -- α< -- 2 -- 3.3 Long-Range Regime, α< -- 1 -- 4 Fast Scrambling and Sparse Models -- 4.1 Sparse Nonlocal Interactions for Fast Scrambling -- 4.2 Sparse Nonlocal Fast Scramblers -- 5 Implementation in Experiments -- 5.1 Long-Range Interactions with Trapped Ions -- 5.2 Long-Range Interactions with Rydberg Atoms -- 5.3 Long-Range Interactions in Cavity Quantum Electrodynamics -- 6 Outlook and Further Connections -- References -- Quantum Map Approach to Entanglement Transfer and Generation in Spin Chains -- 1 Introduction -- 2 Quantum Dynamical Maps -- 3 U(1)-Symmetric Hamiltonians -- 4 One-Qubit Map -- 5 Two-Qubit Map -- 6 Two-Qubit Entanglement Generation -- 7 Four-Qubit Entanglement Generation -- 8 Conclusion -- References -- Weak Ergodicity Breaking Through the Lens of QuantumEntanglement -- 1 Introduction -- 2 Matrix Product State Methods -- 2.1 Towers of Quasiparticles -- 2.2 Time-Dependent Variational Principle -- 3 Mechanisms of Weak Ergodicity Breaking -- 3.1 Spectrum Generating Algebra -- 3.2 Hilbert Space Fragmentation -- 3.3 Projector Embedding -- 4 PXP Model -- 4.1 The Model -- 4.2 Ergodicity Breaking in the PXP Model -- 4.3 The Origin of Non-thermal Eigenstates and Quantum Revivals -- 5 Semiclassical Dynamics -- 5.1 Discussion: Benefits and Pitfalls of TDVP. , 6 Quantum Many-Body Scars.

Additional Edition: ISBN 3-031-03997-1

Language: English

UID:

Format: 1 Online-Ressource (XVI, 541 Seiten)

ISBN: 9783031039980

Series Statement: Quantum science and technology

Content: This book covers recent developments in the understanding, quantification, and exploitation of entanglement in spin chain models from both condensed matter and quantum information perspectives. Spin chain models are at the foundation of condensed matter physics and quantum information technologies and elucidate many fundamental phenomena such as information scrambling, quantum phase transitions, and many-body localization. Moreover, many quantum materials and emerging quantum devices are well described by spin chains. Comprising accessible, self-contained chapters written by leading researchers, this book is essential reading for graduate students and researchers in quantum materials and quantum information. The coverage is comprehensive, from the fundamental entanglement aspects of quantum criticality, non-equilibrium dynamics, classical and quantum simulation of spin chains through to their experimental realizations, and beyond into machine learning applications.

Note: Chapter 1: Entanglement spectra of spin chains -- Chapter 2: Detecting quantum phase transitions in spin chains -- Chapter 3: Entanglement entropy in critical quantum spin chains with boundaries and defects -- Chapter 4: Entanglement entropy and localization in disordered quantum chains -- Chapter 5: Some aspects of Aeck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation -- Chapter 6: Machine-learning-assisted entanglement -- Chapter 7: Local Convertibility in quantum spin -- Chapter 8: Optimal parent Hamiltonians for many-body -- Chapter 9: Entanglement dynamics in hybrid quantum circuits -- Chapter 10: Quantum simulation using noisy unitary circuits and measurements -- Chapter 12: Quantum map approach to entanglement -- Chapter 13: Weak ergodicity breaking through the lens of quantum entanglement -- Chapter 14: Quench dynamics of Rényi negativities -- Chapter 15: Phases and dynamics of ultracold bosons in a tilted optical lattice -- Chapter 16: NMR experimental study of out-of-equilibrium -- Chapter 17: Quantum-dot spin chains.

Additional Edition: ISBN 9783031039973

Additional Edition: ISBN 9783031039997

Additional Edition: ISBN 9783031040009

Additional Edition: Erscheint auch als Druck-Ausgabe Entanglement in spin chains Cham : Springer, 2022 ISBN 9783031039973

Language: English

Keywords: Spinkette ; Verschränkter Zustand

DOI: 10.1007/978-3-031-03998-0

URL: lizenzpflichtig