Topological phases in the theory of solid states
Izvestiya. Mathematics , Tome 87 (2023) no. 5, pp. 1051-1061.

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The paper is a survey devoted to the topological phases – one of the actively developing directions in the theory of solid states. An interpretation of topological phases in terms of the generalized cohomology theories and $K$-theory is given.
Keywords: topological phases, gapped Hamiltonians, generalized cohomology theories.
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A. G. Sergeev; E. Teplyakov. Topological phases in the theory of solid states. Izvestiya. Mathematics , Tome 87 (2023) no. 5, pp. 1051-1061. http://geodesic.mathdoc.fr/item/IM2_2023_87_5_a11/

[1] A. G. Sergeev, “On mathematical problems in the theory of topological insulators”, Theoret. and Math. Phys., 208:2 (2021), 1144–1155 | DOI

[2] I. V. Maresin, A. G. Sergeev, and E. A. Teplyakov, “On mathematical aspects of the theory of topological insulators”, Acta Math. Sin. (Engl. Ser.) (to appear)

[3] A. Kapustin, Symmetry protected topological phases, anomalies, and cobordisms: beyond group cohomology, arXiv: 1403.1467v3

[4] D. S. Freed and M. J. Hopkins, Reflection positivity and invertible topological phases, arXiv: 1604.06527v5

[5] Xie Chen, Zheng-Cheng Gu, Zheng-Xin Liu, and Xiao-Gang Wen, “Symmetry protected topological orders and the group cohomology of their symmetry group”, Phys. Rev. B, 87:15 (2013), 155114 | DOI

[6] C. Bourne and Y. Ogata, “The classification of symmetry protected topological phases of one-dimensional fermion systems”, Forum Math. Sigma, 9 (2021), e25 | DOI | MR | Zbl

[7] D. Gaiotto and T. Johnson-Freyd, Symmetry protected topological phases and generalized cohomology, arXiv: 1712.07950v2

[8] Xiao-Liang Qi, T. L. Hughes, and Shou-Cheng Zhang, “Topological field theory of time-reversal invariant insulators”, Phys. Rev. B, 78:19 (2008), 195424 | DOI

[9] C. Z. Xiong, “Minimalist approach to the classification of symmetry protected topological phases”, J. Phys. A, 51:44 (2018), 445001 | DOI | MR | Zbl

[10] Z. Xiong, Classification and construction of topological phases of quantum matter, arXiv: 1906.02892v1

[11] Guo Chuan Thiang, “On the $K$-theoretic classification of topological phases of matter”, Ann. Henri Poincaré, 17:4 (2016), 757–794 | DOI | MR | Zbl

[12] A. Hatcher, Algebraic topology, Cambridge Univ. Press, Cambridge, 2002 | MR | Zbl

[13] A. Kitaev, On the classification of short-range entangled states, Topological Phases of Matter, Stony Brook University, 2013