Entanglement in many-body systems

By Luigi Amico, Rosario Fazio, A. Osterloh, Vlatko Vedral. 2007

2,717 citations recorded by the source corpus.

Recent interest in aspects common to quantum information and condensed matter has prompted a flurry of activity at the border of these disciplines that were far distant until a few years ago. Numerous interesting questions have been addressed so far. Here an important part of this field, the properties of the entanglement in many-body systems, are reviewed. The zero and finite temperature properties of entanglement in interacting spin, fermion, and boson model systems are discussed. Both bipartite and multipartite entanglement will be considered. In equilibrium entanglement is shown tightly connected to the characteristics of the phase diagram. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium entangled states are generated and manipulated by means of many-body Hamiltonians.

View Paper: https://www.semanticscholar.org/paper/81c9d54c68653dabe6fbdbe3f79a0ea3bdbfc46b

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Citations in the corpus

Tensor product methods and entanglement optimization for ab initio quantum chemistry (2014, unknown): “n=0, sz=0 n=1, sz=- 1 2 n=1, sz= 1 2 n=2, sz=-1 n=2, sz=0 n=2, sz=1 n=3, sz=- 1 2 n=3, sz= 1 2 n=4, sz=0 ρi,j −− − ↓ ↓− −↑ ↑− ↓ ↓ −↑↓ ↓ ↑ ↑ ↓ ↑↓− ↑ ↑ ↓ ↑↓ ↑↓ ↓ ↑ ↑↓ ↑↓ ↑ ↑↓ ↑↓ −− (1,1) − ↓ (1,6) (2,5) ↓− (5,2) (6,1) −↑ (1,11) (3,9) ↑− (9,3) (1,11) ↓ ↓ (6,6) −↑↓ (1,16) (2,15) (3,14) (4,13) ↓ ↑ (5,12)”
Entanglement certification from theory to experiment (2018, methodology): “In the former case the celebrated area law of entanglement for non-critical systems emerged as a major result and the corresponding classification of entangled states as tensor networks, a notion closely connected to classical simulability of many-body states [46–51].”
Gapless Symmetry-Protected Topological Order (2017, background): “[127] Luigi Amico, Rosario Fazio, Andreas Osterloh, and Vlatko Vedral, “Entanglement in many-body systems,” Rev.”
Geometry of Quantum States: Index (2007, background): “30 Many good reviews exist [31, 903], and a forthcoming book by Zeng, Chen, Zhou and Wen [998] describes how quantum information meets quantum matter.”
Entanglement entropy and conformal field theory (2009, background): “For a comprehensive treatment of these aspects we refer the reader to the other reviews in this special issue [4] and to the already existing ones [5, 6].”
Entanglement dynamics after quantum quenches in generic integrable systems (2017, background): “The standard measure of the entanglement is the entanglement entropy [68] which is defined as the von Neumann entropy of the reduced density matrix (1): S ≡ −TrρA ln ρA.”
Spreading of correlations and entanglement after a quench in the one-dimensional Bose–Hubbard model (2008, background): “In recent years many different measures have been proposed for the entanglement in a system [1].”