The DOI matches its Crossref record.
Universal noninteger ‘‘ground-state degeneracy’’ in critical quantum systems
Abstract
One-dimensional critical quantum sytems have a universal, intensive ``ground-state degeneracy,'' g, which depends on the universality class of the boundary conditions, and is in general noninteger. This is calculated, using the conjectured boundary conditions corresponding to a multichannel Kondo impurity and shown to agree with Bethe-ansatz results. g is argued to decrease under renormalization from a less stable to a more stable critical point and plays a role in boundary critical phenomena quite analogous to that played by c, the conformal anomaly, in the bulk case.
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
No references could be resolved yet.
Research works printed but not linked: 15
- H. W. J. Blöte, 1986, Phys. Rev. Lett., 56, 742, 10.1103/PhysRevLett.56.742 · DOI · Paper page
- I. Affleck, 1986, Phys. Rev. Lett., 56, 746, 10.1103/PhysRevLett.56.746 · DOI · Paper page
- J. L. Cardy, 1989, Nucl. Phys., B324, 581, 10.1016/0550-3213(89)90521-X · DOI · Paper page
- I. Affleck, 1990, Nucl. Phys., B336, 517, 10.1016/0550-3213(90)90440-O · doi:10.1016/0550-3213(90)90440-o
- I. Affleck, 1991, Nucl. Phys., B352, 849, 10.1016/0550-3213(91)90109-B · DOI · Paper page
- D. Altschüler, 1990, Commun. Math. Phys., 132, 349, 10.1007/BF02096653 · doi:10.1007/bf02096653
- V. G. Kac, 1984, Adv. Math., 53, 125, 10.1016/0001-8708(84)90032-X · DOI · Paper page
- A. A. Belavin, 1984, Nucl. Phys., B241, 333, 10.1016/0550-3213(84)90052-X · DOI · Paper page
- E. Verlinde, 1988, Nucl. Phys., B300, 360, 10.1016/0550-3213(88)90603-7 · DOI · Paper page
- A. M. Tsvelick, 1985, J. Phys. C, 18, 159, 10.1088/0022-3719/18/1/020 · doi:10.1088/0022-3719/18/1/020
- N. Andrei, 1984, Phys. Rev. Lett., 52, 364, 10.1103/PhysRevLett.52.364 · doi:10.1103/physrevlett.52.364
- C. L. Seaman, 1991, Bull. Am. Phys. Soc., 36, 556
- P. Nozie`res, 1980, J. Phys. (Paris), 41, 193, 10.1051/jphys:01980004103019300 · DOI · Paper page
- A. W. W. Ludwig, 1987, Nucl. Phys., B285, 97, 10.1016/0550-3213(87)90330-0 · DOI
- A. B. Zamolodchikov, 1986, JETP Lett., 43, 730
Cited by
Entanglement in many-body systems
Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745
Entanglement entropy and quantum field theory
Calabrese, P., & Cardy, J. (2004) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2004/06/p06002 · Cited by 3,275
Entanglement Entropy and Quantum Field Theory
Calabrese, P., & Cardy, J. (2004) · arXiv · doi:10.48550/arxiv.hep-th/0405152 · Cited by 3,275
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
The Page curve of Hawking radiation from semiclassical geometry
Almheiri, A., Mahajan, R., Maldacena, J., & Zhao, Y. (2020) · Journal of High Energy Physics · doi:10.1007/jhep03(2020)149 · Cited by 898
Metadata
- Authors
- Affleck, I., & Ludwig, A. W. W.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1991-07-08
- Volume
- 67
- Issue
- 2
- Pages
- 161-164
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2094219754
- Cited by
- 999
- References
- 0
- FWCI
- 8.45
- Type
- journal article
- Language
- en
- Open access
- closed
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 noninteger ‘‘ground-state degeneracy’’ in critical quantum systems. https://app.cochat.ai/papers/10.1103/physrevlett.67.161
- The paper
- Affleck, I., & Ludwig, A. W. W. (1991). Universal noninteger ‘‘ground-state degeneracy’’ in critical quantum systems. Physical Review Letters. https://doi.org/10.1103/physrevlett.67.161
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.