The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Interacting topological phases and modular invariance
Open accessAbstract
We discuss (2+1)-dimensional topological superconductors with ${N}_{f}$ left- and right-moving Majorana edge modes and a ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ symmetry. In the absence of interactions, these phases are distinguished by an integral topological invariant ${N}_{f}$. With interactions, the edge state in the case of ${N}_{f}=8$ is unstable against interactions, and a ${\mathbb{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{2}$ invariant mass gap can be generated dynamically. We show that this phenomenon is closely related to the modular invariance of type II superstring theory. More generally, we show that the global gravitational anomaly of the nonchiral Majorana edge states is the physical manifestation of the bulk topological superconductors classified by ${\mathbb{Z}}_{8}$.
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
Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
Self-citationQuantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
Bernevig, B. A., Hughes, T. L., & Zhang, S.-C. (2006) · Science · doi:10.1126/science.1133734 · Cited by 7,090
Self-citationZ 2 Topological Order and the Quantum Spin Hall Effect
Kane, C. L., & Mele, E. J. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.146802 · Cited by 6,460
Anyons in an exactly solved model and beyond
Kitaev, A. (2006) · Annals of Physics · doi:10.1016/j.aop.2005.10.005 · Cited by 5,245
Topological Insulators in Three Dimensions
Fu, L., Kane, C. L., & Mele, E. J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.106803 · Cited by 4,651
Topological insulators with inversion symmetry
Fu, L., & Kane, C. L. (2007) · Physical Review B · doi:10.1103/physrevb.76.045302 · Cited by 4,252
Topological field theory of time-reversal invariant insulators
Qi, X.-L., Hughes, T. L., & Zhang, S.-C. (2008) · Physical Review B · doi:10.1103/physrevb.78.195424 · Cited by 3,329
Self-citationOperator content of two-dimensional conformally invariant theories
Cardy, J. L. (1986) · Nuclear Physics B · doi:10.1016/0550-3213(86)90552-3 · Cited by 1,955
Helical Liquid and the Edge of Quantum Spin Hall Systems
Wu, C., Bernevig, B. A., & Zhang, S.-C. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.106401 · Cited by 759
Self-citationStability of the quantum spin Hall effect: Effects of interactions, disorder, andZ2topology
Xu, C., & Moore, J. E. (2006) · Physical Review B · doi:10.1103/physrevb.73.045322 · Cited by 571
Cited by
Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Self-citationSymmetry fractionalization, defects, and gauging of topological phases
Barkeshli, M., Bonderson, P., Cheng, M., & Wang, Z. (2019) · Physical Review B · doi:10.1103/physrevb.100.115147 · Cited by 533
Higher-order topological insulators and superconductors protected by inversion symmetry
Khalaf, E. (2018) · Physical Review B · doi:10.1103/physrevb.97.205136 · Cited by 528
Topological Superconductivity in Twisted Multilayer Graphene
Xu, C., & Balents, L. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.087001 · Cited by 430
Fidkowski, L., Chen, X., & Vishwanath, A. (2013) · Physical Review X · doi:10.1103/physrevx.3.041016 · Cited by 272
Metadata
- Authors
- Ryu, S., & Zhang, S.-C.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2012-06-27
- Volume
- 85
- Issue
- 24
- ISSN
- 1098-0121 (ISSN-L)
- 1550-235X
- OpenAlex
- W1984334615
- Cited by
- 213
- References
- 11
- FWCI
- 7.31
- 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: Interacting topological phases and modular invariance. https://app.cochat.ai/papers/10.1103/physrevb.85.245132
- The paper
- Ryu, S., & Zhang, S.-C. (2012). Interacting topological phases and modular invariance. Physical Review B. https://doi.org/10.1103/physrevb.85.245132
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.
