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Keywords
(14)
Black Hole Physics
Decay of Correlations
Degree of Freedom
Disordered System
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Quantum Information
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Scaling Law
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Colloquium: Area laws for the entanglement entropy
Colloquium: Area laws for the entanglement entropy,10.1103/RevModPhys.82.277,Reviews of Modern Physics,J. Eisert,M. Cramer,M. B. Plenio
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Colloquium: Area laws for the entanglement entropy
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Citations: 4
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J. Eisert
,
M. Cramer
,
M. B. Plenio
Physical interactions in quantum manybody systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such ``area laws'' for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of
black hole
physics,
quantum information
science, and quantum manybody physics where they have important implications on the
numerical simulation
of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrixproduct states, higherdimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.
Journal:
Reviews of Modern Physics  REV MOD PHYS
, vol. 82, no. 1, pp. 277306, 2010
DOI:
10.1103/RevModPhys.82.277
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Citations
(4)
Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
Beni Yoshida
,
Beni
Journal:
Annals of Physics  ANN PHYS N Y
, vol. 326, no. 1, pp. 1595, 2011
The trilinear Hamiltonian: a zerodimensional model of Hawking radiation from a quantized source
Paul D. Nation
,
Miles P. Blencowe
Journal:
New Journal of Physics  NEW J PHYS
, vol. 12, no. 9, 2010
Geometric entanglement in valancebondsolid state
H. T. Cui
,
C. M. Wang
,
S. Z. Yuan
Journal:
European Physical Journal B  EUR PHYS J B
, vol. 74, no. 4, pp. 543553, 2010
Mutual information in classical spin models
Johannes Wilms
,
Matthias Troyer
,
Frank Verstraete
Published in 2010.