The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Universal terms for the entanglement entropy in 2+1 dimensions
Open accessAbstract
Abstract We show that the entanglement entropy and alpha entropies corresponding to spatial polygonal sets in 2 + 1 dimensions contain a term which scales logarithmically with the cutoff. Its coefficient is a universal quantity consisting in a sum of contributions from the individual vertices. For a free scalar field this contribution is given by the trace anomaly in a three-dimensional space with conical singularities located on the boundary of a plane angular sector. We find its analytic expression as a function of the angle. This is given in terms of the solution of a set of non-linear ordinary differential equations. For general free fields, we also find the small-angle limit of the logarithmic coefficient, which is related to the two-dimensional entropic c-functions. The calculation involves a reduction to a two-dimensional problem, and as a byproduct, we obtain the trace of the Green function for a massive scalar field in a sphere where boundary conditions are specified on a segment of a great circle. This also gives the exact expression for the entropies for a scalar field in a two-dimensional de Sitter space.
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.
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
Ryu, S., & Takayanagi, T. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.181602 · Cited by 4,302
Entanglement Entropy and Quantum Field Theory
Calabrese, P., & Cardy, J. (2004) · arXiv · doi:10.48550/arxiv.hep-th/0405152 · Cited by 3,275
Entanglement in Quantum Critical Phenomena
Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.227902 · Cited by 2,793
Scaling of entanglement close to a quantum phase transition
Osterloh, A., Amico, L., Falci, G., & Fazio, R. (2002) · Nature · doi:10.1038/416608a · Cited by 1,860
Entanglement in a simple quantum phase transition
Osborne, T. J., & Nielsen, M. A. (2002) · Physical Review A · doi:10.1103/physreva.66.032110 · Cited by 1,472
Quantum source of entropy for black holes
Bombelli, L., Koul, R. K., Lee, J., & Sorkin, R. D. (1986) · Physical Review D · doi:10.1103/physrevd.34.373 · Cited by 1,439
On the quantum structure of a black hole
't Hooft, G. (1985) · Nuclear Physics B · doi:10.1016/0550-3213(85)90418-3 · Cited by 1,311
Complex powers of an elliptic operator
Seeley, R. T. (1967) · Proceedings of Symposia in Pure Mathematics · doi:10.1090/pspum/010/0237943 · Cited by 1,032
Callan, C., & Wilczek, F. (1994) · Physics Letters B · doi:10.1016/0370-2693(94)91007-3 · Cited by 826
Entanglement and alpha entropies for a massive Dirac field in two dimensions
Casini, H., Fosco, C. D., & Huerta, M. (2005) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2005/07/p07007 · Cited by 293
Self-citation
Cited by
Colloquium : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873
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
Quantum entanglement in condensed matter systems
Laflorencie, N. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.06.008 · Cited by 765
Entanglement entropy in free quantum field theory
Casini, H., & Huerta, M. (2009) · Journal of Physics A: Mathematical and Theoretical · doi:10.1088/1751-8113/42/50/504007 · Cited by 752
Self-citationMeasuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations
Hastings, M. B., González, I., Kallin, A. B., & Melko, R. G. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.157201 · Cited by 427
Metadata
- Authors
- Casini, H., & Huerta, M.
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 2007-03
- Volume
- 764
- Issue
- 3
- Pages
- 183-201
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W1990045935
- Cited by
- 212
- References
- 11
- FWCI
- 4.03
- Type
- journal article
- Language
- en
- Open access
- green
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Universal terms for the entanglement entropy in 2+1 dimensions. https://app.cochat.ai/papers/10.1016/j.nuclphysb.2006.12.012
- The paper
- Casini, H., & Huerta, M. (2007). Universal terms for the entanglement entropy in 2+1 dimensions. Nuclear Physics B. https://doi.org/10.1016/j.nuclphysb.2006.12.012
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
