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 d = 1 and generally false in d 1. Therefore, Theorem 1.5 is false in dimension d 1—under the stated assumptions in Ref. 2, 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 Ref. 2, namely, Theorems 1.6–1.8 only hold once we impose.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics