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Erratum to: “Classification of Hamiltonians in neighborhoods of band crossings in terms of the theory of singularities”. (English) Zbl 1435.82029

From the text: In a recent paper, we reported the classification of Hamiltonians in neighborhoods of band crossings in terms of the theory of singularities. In the derivation in p. 31, Appendix B: Case \(D = 0\) in Sec. IV B 4, the 11th line from the top, we wrote, “In this case, we can show that \(a = b = 0\) by using a proof by contradiction.” However, this statement is not correct because if we put \((p_{21}, p_{22}, p_{23}) = (1, 0, 0)\) and \((p_{31}, p_{32}, p_{33}) = (0, 1, 0), Q(k_2, k_3) = 2k^2_2 \), we can find \(a, b \in \mathbb{R}\) in Eq. (B4). This error leads to an omission of the other possibilities which are now stated here.
©2019 American Institute of Physics
This erratum concerns the authors’ paper [ibid. 58, No. 7, 073502, 39 p. (2017; Zbl 1370.82042)].

MSC:

82D20 Statistical mechanics of solids
82D37 Statistical mechanics of semiconductors
82D35 Statistical mechanics of metals
35P05 General topics in linear spectral theory for PDEs
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory

Citations:

Zbl 1370.82042
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References:

[1] Teramoto, H.; Kondo, K.; Izumiya, S.; Toda, M.; Komatsuzaki, T., Classification of Hamiltonians in neighborhoods of band crossings in terms of the theory of singularities, J. Math. Phys., 58, 073502 (2017) · Zbl 1370.82042
[2] Teramoto, H., Tsuchida, A., Kondo, K., Izumiya, S., Toda, M., and Komatsuzaki, T., “Application of singularity theory to bifurcation of band structures in crystals,” J. Sing. (submitted). · Zbl 1370.82042
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