A short review on entanglement in quantum spin systems

Abstract

We review some of the recent progress on the study of entropy of entanglement in many-body quantum systems. Emphasis is placed on the scaling properties of entropy for one-dimensional multi-partite models at quantum phase transitions and, more generally, on the concept of area law. We also briefly describe the relation between entanglement and the presence of impurities, the idea of particle entanglement, the evolution of entanglement along renormalization group trajectories, the dynamical evolution of entanglement and the fate of entanglement along a quantum computation.

20 pages and 6 figures. Review article for the special issue "Entanglement entropy in extended systems" in J. Phys. A, edited by P. Calabrese, J. Cardy and B. Doyon

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• Particle Number Fluctuations, Rényi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization
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• Entanglement spectrum of random-singlet quantum critical points
• Solution of the fermionic entanglement problem with interface defects
• Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States
• Factorization and Criticality in the Anisotropic XY Chain via Correlations
• Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Excited-state entanglement and thermal mutual information in random spin chains
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• Bi-partite entanglement entropy in massive 1+1-dimensional quantum field theories
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Quantum coherence of planar spin models with Dzyaloshinsky-Moriya interaction
• On the relation between entanglement and subsystem Hamiltonians
• The entanglement entropy of 1D systems in continuous and homogenous space
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• Growth of mutual information in a quenched one-dimensional open quantum many body system
• Symmetry-resolved entanglement in a long-range free-fermion chain
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• Multipartite Entanglement Accumulation in Quantum States: Localizable Generalized Geometric Measure
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• Entanglement of inhomogeneous free fermions on hyperplane lattices
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• Quantum Fisher Information and multipartite entanglement in spin-1 chains
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• Magnetic field dependence of the entanglement entropy of one dimensional spin systems in quantum phase transition induced by a quench
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Extracting many-particle entanglement entropy from observables using supervised machine learning
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• Entanglement entropy in Fermi gases and Anderson's orthogonality catastrophe
• Measuring the tangle of three-qubit states
• Logarithmic, Fractal and Volume-Law Entanglement in a Kitaev chain with long-range hopping and pairing
• Fidelity susceptibility of one-dimensional models with twisted boundary conditions
• On the closedness and geometry of tensor network state sets
• Ground-state phase diagram of the frustrated spin-1/2 two-leg honeycomb ladder
• Entanglement of Free Fermions on Johnson Graphs
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• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
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