Entanglement and tensor network states

Abstract

These lecture notes provide a brief overview of methods of entanglement theory applied to the study of quantum many-body systems, as well as of tensor network states capturing quantum states naturally appearing in condensed-matter systems.

Invited lecture notes for the "Autumn School on Correlated Electrons: Emergent Phenomena in Correlated Matter", E. Pavarini, E. Koch, and U. Schollwoeck Eds., Juelich, September 23-27, 2013. 39 pages, 33 figures (v2: reference added)

References in corpus (7)

• Negativity and topological order in the toric code
• Infinite size density matrix renormalization group, revisited
• Stochastic Error Cancellation in Analog Quantum Simulation
• Robustness in Projected Entangled Pair States
• Grassmann tensor network states and its renormalization for strongly correlated fermionic and bosonic states
• Condensed Matter Applications of Entanglement Theory
• Stability of the Area Law for the Entropy of Entanglement

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• Time evolution of many-body localized systems in two spatial dimensions
• Multidimensional approximation of nonlinear dynamical systems
• How an autonomous quantum Maxwell demon can harness correlated information
• Tensor Network Contractions for #SAT
• Scaling of neural-network quantum states for time evolution
• Lectures on Quantum Tensor Networks
• Efficient variational contraction of two-dimensional tensor networks with a non-trivial unit cell
• Quantum Machine Learning Tensor Network States
• Mutual Information Scaling for Tensor Network Machine Learning
• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• Surrogate models for quantum spin systems based on reduced order modeling
• Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states
• Symmetry-resolved entanglement of 2D symmetry-protected topological states
• Residual Matrix Product State for Machine Learning
• Estimation of correlations and non-separability in quantum channels via unitarity benchmarking
• Rényi entanglement entropy of spin chain with Generative Neural Networks
• A Tensor Network Approach to Finite Markov Decision Processes
• Entanglement Properties of Quantum Superpositions of Smooth, Differentiable Functions
• Fibre Lasers for Gamma Colliders
• Non-chiral bosonization of strongly inhomogeneous Luttinger liquids
• Pushing Tensor Networks to the Limit