The DOI matches its Crossref record; 249 of the 249 references it cites were found in a registry or an index.
Colloquium : Area laws for the entanglement entropy
Open accessAbstract
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 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 many-body 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. Matrix-product states, higher-dimensional 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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Indeed, this fact is related to correlation and entanglement spreading according to the Lieb-Robinson theorem that states that, after a sufficiently large time, states can become strongly entangled ([91-96], see also [97]).”
From Can one trust quantum simulators? (2012) · cites this paper as [95]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 25,904
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
Anti de Sitter space and holography
Witten, E. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n2.a2 · Cited by 13,070
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118
Many-body physics with ultracold gases
Bloch, I., Dalibard, J., & Zwerger, W. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.885 · Cited by 8,114
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
Bekenstein, J. D. (1973) · Physical Review D · doi:10.1103/physrevd.7.2333 · Cited by 7,555
Fault-tolerant quantum computation by anyons
Kitaev, A. Y. (2003) · Annals of Physics · doi:10.1016/s0003-4916(02)00018-0 · Cited by 7,238
Large N field theories, string theory and gravity
Ofer Aharony, A., Gubser, S. S., MALDACENA, J. M., Ooguri, H., & Oz, Y. (2000) · Physics Reports · doi:10.1016/s0370-1573(99)00083-6 · Cited by 6,327
HAWKING, S. W. (1974) · Nature · doi:10.1038/248030a0 · Cited by 5,669
Research works printed but not linked: 5
- Anders, J., 2008, Quantum Inf. Comput., 8, 0245
- Its, A. R., 2007, Fields Inst. Commun., 50, 151
- Latorre, J. I., 2004, Quantum Inf. Comput., 4, 48
- 1999, Density-Matrix Renormalization, A New Numerical Method in Physics
- Plenio, M. B., 2007, Quantum Inf. Comput., 7, 1
Cited by
Sorted by citations
Entanglement entropy and conformal field theory
Calabrese, P., & Cardy, J. (2009) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504005 · Cited by 1,688
“I (n) A:B does not have all the correct properties to be an entanglement measure (see the review by Amico and Fazio in this special issue [8] for a discussion of various entanglement measures), but it has the fundamental property of satisfying the area law [6, 9], even at finite temperature [10].”
BackgroundThe classical-quantum boundary for correlations: Discord and related measures
Modi, K., Brodutch, A., Cable, H., Paterek, T., & Vedral, V. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1655 · Cited by 1,600
Quantum Chemistry in the Age of Quantum Computing
Cao, Y., Romero, J., Olson, J. P., Degroote, M., Johnson, P. D., Kieferová, M., Kivlichan, I. D., Menke, T., Peropadre, B., Sawaya, N. P. D., et al. (2019) · Chemical Reviews · doi:10.1021/acs.chemrev.8b00803 · Cited by 1,560
Albash, T., & Lidar, D. A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015002 · Cited by 1,546
Light-cone-like spreading of correlations in a quantum many-body system
Cheneau, M., Barmettler, P., Poletti, D., Endres, M., Schauß, P., Fukuhara, T., Gross, C., Bloch, I., Kollath, C., & Kuhr, S. (2012) · Nature · doi:10.1038/nature10748 · Cited by 864
Metadata
- Authors
- Eisert, J., Cramer, M., & Plenio, M. B.
- Affiliations
- University of Potsdam (DE)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2010-02-04
- Volume
- 82
- Issue
- 1
- Pages
- 277-306
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W1922629554
- Cited by
- 2,873
- References
- 249
- Citations by year
- 2026: 164 · 2025: 232 · 2024: 229 · 2023: 204 · 2022: 225 · 2021: 196 · 2020: 206 · 2019: 205 · 2018: 169 · 2017: 163 · 2016: 166 · 2015: 158 · 2014: 163 · 2013: 141 · 2012: 99
- FWCI
- 64.56
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- publish.UP (University of Potsdam) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- area law, entanglement entropy, quantum many-body systems, lattice model, ground state, thermal states, disordered systems, non-equilibrium states, topological entanglement entropy, matrix product states, entanglement renormalization, correlation functions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
