×

Erratum to: “Exponentially localized Wannier functions in periodic zero flux magnetic fields”. (English) Zbl 1454.82040

From the text: A reader informed us of an error in Theorem 3.3, which characterizes magnetic symmetries; more precisely, items (ii) and (iii) are only true in \(\mathrm{d} = 1\) and generally false in \(\mathrm{d} > 1\). Therefore, Theorem 1.5 is false in dimension \(\mathrm{d} > 1\) – under the stated assumptions in our paper, the existence of a magnetic time-reversal symmetry is not automatic. Indeed, the Haldane model is an explicit counterexample in dimension 2.3. Consequently, we need to add this as an extra hypothesis to our assumptions in our main results of our paper, namely, Theorems 1.6–1.8. only once we impose a further assumption which we describe in the following.
Erratum to the authors’ paper [ibid. 52, No. 11, 112103, 32 p. (2011; Zbl 1272.82036)].

MSC:

82D20 Statistical mechanics of solids
82D40 Statistical mechanics of magnetic materials
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)

Citations:

Zbl 1272.82036
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] De Nittis, G.; Lein, M., Rev. Math. Phys., 23, 233 (2011) · Zbl 1214.81093
[2] De Nittis, G.; Lein, M., J. Math. Phys., 52, 112103 (2011) · Zbl 1272.82036
[3] Haldane, F. D. M., Phys. Rev. Lett., 61, 2015 (1988)
[4] Lee, C. H.; Wang, Y.; Chen, Y.; Zhang, X., Phys. Rev. B, 98, 094434 (2018)
[5] Nenciu, G., Rev. Mod. Phys., 63, 91-127 (1991)
[6] Ozawa, T.; Price, H. M.; Goldman, N.; Zilberberg, O.; Carusotto, I., Phys. Rev. A, 93, 043827 (2016)
[7] Petrides, I.; Price, H. M.; Zilberberg, O., Phys. Rev. B, 98, 125431 (2018)
[8] Zilberberg, O.; Huang, S.; Guglielmon, J.; Wang, M.; Chen, K. P.; Kraus, Y. E.; Rechtsman, M. C., Nature, 553, 59-62 (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.