CoChat
Sign Up
Cited by 600Topological Materials and PhenomenaQuantum and electron transport phenomenaAdvanced Condensed Matter Physics

Homotopy and Quantization in Condensed Matter Physics

Avron, J. E., Seiler, R., Simon, B.·1983·Physical Review Letters
DOI 10.1103/physrevlett.51.51
Open this paper in CoChat — free account

Abstract

It is shown that the integers found by Thouless et al. in the quantized Hall effect are the only quantized quantities associated with the energy bands. It is also proved that if two bands touch and then come apart as a parameter is varied, then their individual integers (conductances) may not be preserved but their sum is preserved.

Integrity signals

Registry

Crossref · 10.1103/physrevlett.51.51

Cites

6 of 6 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

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?

  • Closing and reopening of lower gaps may change the Chern number of specific bands, but their sum is unaffected.

    “On the other hand, closing and reopening of the lower gaps may change the Chern number of the specific bands in question, but their sum is unaffected [22].”

    From Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems (2022) · cites this paper as [22]

  • A generalization of the homotopy argument of Avron, Seiler, and Simon can be used to show that there are three Chern numbers per band in three dimensions, associated with the xy, yz, and xz planes of the Brillouin zone.

    “A generalization of the previously mentioned homotopy argument of Avron, Seiler, and Simon (56) can be used to show that there are three Chern numbers per band in three dimensions, associated with the xy , yz , and xz planes of the Brillouin zone.”

    From Three-Dimensional Topological Insulators (2011) · cites this paper as [56]

  • The four-band model on a cubic lattice by Hosur et al. is in the strong topological phase when |t| < |m| < 3|t| and λ=0.

    “This Hamiltonian is in the strong topological phase when | t | &lt; | m | &lt; 3 | t | and λ = 0, with the time-reversal operator represented by -iσ y K .”

    From Antiferromagnetic topological insulators (2010) · cites this paper as [28]

Cites

Flagged first, then by citations

Cited by

Sorted by citations

Related

Authors
Avron, J. E., Seiler, R., & Simon, B.
Affiliations
California Institute of Technology (US)
ORCID
Avron, J. E.
Venue
Physical Review Letters
Publisher
American Physical Society (APS)
Published
1983-07-04
Volume
51
Issue
1
Pages
51-53
ISSN
0031-9007 (ISSN-L)
DOI
10.1103/physrevlett.51.51
OpenAlex
W1988195577
Cited by
600
References
6
Citations by year
2026: 14 · 2025: 19 · 2024: 24 · 2023: 27 · 2022: 24 · 2021: 37 · 2020: 56 · 2019: 19 · 2018: 26 · 2017: 23 · 2016: 21 · 2015: 12 · 2014: 19 · 2013: 20 · 2012: 12
FWCI
5.19
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review Letters (publishedVersion)
  • CaltechAUTHORS (California Institute of Technology) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
Keywords
integer quantum Hall effect, homotopy, topological invariants, electronic band structure, band touching, conductance quantization, topological phase transition

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