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2014 | 1 | 1 |

Article title

The Non-Commutative Geometry of the Complex Classes of Topological Insulators

Authors

Content

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EN

Abstracts

EN
Alain Connes’ Non-Commutative Geometry program
[1] has been recently carried out [2, 3] for the entire
A- and AIII-symmetry classes of topological insulators,
in the regime of strong disorder where the insulating
gap is completely filled with dense localized spectrum.
This is a short overview of these results, whose goal is to
highlight the methods of Non-Commutative Geometry involved
in these studies. The exposition proceeds gradually
through the cyclic cohomology, quantized calculus with
Fredholm-modules, local formulas for the odd and even
Chern characters and index theorems for the odd and even
Chern numbers. The characterization of the A- and AIIIsymmetry
classes in the presence of strong disorder and
magnetic fields emerges as a natural application of these
tools.

Publisher

Year

Volume

1

Issue

1

Physical description

Dates

received
23 - 2 - 2014
online
30 - 6 - 2014
accepted
6 - 6 - 2014

Contributors

author
  • Department of Physics,
    Yeshiva University, 245 Lexington Av, 10016 New York, USA

References

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  • [2] E. Prodan, B. Leung, and J. Bellissard, J. Phys. A: Math. Theor.46, 485202 (2013).
  • [3] E. Prodan and H. Schulz-Baldes,http://arxiv.org/abs/1402.5002.
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  • [21] J. Bellissard, in Geometric and Topological Methods for QuantumField Theory (World Sci. Publ., River Edge, NJ, 2003), pp.86–156.
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  • [26] E. Prodan, Phys. Rev. B 80, 125327 (2009).
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Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_topor-2014-0001
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