Area laws for the entanglement entropy - a review

@article{Eisert2010AreaLF,
  title={Area laws for the entanglement entropy - a review},
  author={Jens Eisert and Marcus Cramer and Martin Bodo Plenio},
  journal={Reviews of Modern Physics},
  year={2010},
  volume={82},
  pages={277-306}
}
Physical interactions in quantum many-body 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… 

Figures from this paper

Rényi entropy of highly entangled spin chains
TLDR
The Rényi entropy is first analytically computed of the Motzkin and Fredkin models by careful treatment of asymptotic analysis, and is found to be a novel phase transition never seen in any other spin chain studied so far.
Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations
  • Jaeyoon Cho
  • Computer Science, Physics
    Physical Review X
  • 2018
TLDR
This paper dramatically reduces the previously known bound on the entanglement entropy, bringing it, for the first time, into a realistic regime, and discusses the underlying physical picture, based on a renormalization-like construction underpinning the proof, which transforms the entangled entropy of a continuous region into a sum of mutual informations in different length scales and the entangling entropy at the boundary.
Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
In the spectrum of many-body quantum systems appearing in condensed matter physics, the low-energy eigenstates were the traditional focus of research. The interest in the statistical properties of
Entanglement susceptibility: area laws and beyond
Generic quantum states in the Hilbert space of a many-body system are nearly maximally entangled whereas low-energy physical states are not; the so-called area laws for quantum entanglement are
Volume-law scaling for the entanglement entropy in spin-1/2 chains
Entanglement entropy obeys area law scaling for typical physical quantum systems. This may naively be argued to follow from the locality of interactions. We show that this is not the case by
Novel quantum phase transition from bounded to extensive entanglement
TLDR
This work has uncovered a unique, physically transparent quantum phase transition in a spin chain where entanglement entropy itself jumps from low scaling, most typical for gapped models and short-range correlations, to a critical phase where the scaling exhibits an extraordinary amount ofEntanglement.
Area laws in a many-body localized state and its implications for topological order
The question whether Anderson insulators can persist to finite-strength interactions—a scenario dubbed many-body localization—has recently received a great deal of interest. The origin of such a
Entanglement area law in superfluid 4He
When the entropy of a system scales as a function of its surface area, rather than its volume, it is said to obey an entropy area law. Now, an area law is shown to exist numerically in the
Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
A quantum quench is the simplest protocol to investigate nonequilibrium many-body quantum dynamics. Previous studies on the entanglement properties of quenched quantum many-body systems mainly focus
...
...

References

SHOWING 1-10 OF 478 REFERENCES
Entanglement-area law for general bosonic harmonic lattice systems (14 pages)
We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic-lattice system in the ground or a thermal state scale at
Statistics dependence of the entanglement entropy.
TLDR
This work establishes scaling laws for entanglement in critical quasifree fermionic and bosonic lattice systems, without resorting to numerical means, and finds Lifshitz quantum phase transitions accompanied with a nonanalyticity in the prefactor of the leading order term.
Black hole entropy from entanglement: a review
We review aspects of the thermodynamics of black holes and in particular take into account the fact that the quantum entanglement between the degrees of freedom of a scalar field, traced inside the
Entanglement in many-body systems
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.
Critical and noncritical long-range entanglement in Klein-Gordon fields
We investigate the entanglement between two spatially separated intervals in the vacuum state of a free one-dimensional Klein-Gordon field by means of explicit computations in the continuum limit of
Area laws in quantum systems: mutual information and correlations.
TLDR
This Letter shows that the holographic principle not only emerges in the search for new Planck-scale laws but also in lattice models of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law.
Evolution of entanglement entropy following a quantum quench : Analytic results for the XY chain in a transverse magnetic field
The non-equilibrium evolution of extended quantum systems is one of the most challenging problems of contemporary research in theoretical physics. The subject is in a renaissance era after the
Area law for the entropy of low-energy states
It is often observed in the ground state of quantum lattice systems with local interactions that the entropy of a large region is proportional to its surface area. In some cases, this area law is
Entanglement entropy and quantum field theory
We carry out a systematic study of entanglement entropy in relativistic quantum field theory. This is defined as the von Neumann entropy SA = −Tr ρAlogρA corresponding to the reduced density matrix
...
...