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Kagome antiferromagnets display a host of exotic magnetic phenomena originating from a massive degeneracy of classical ground states. Presumably, this massive degeneracy is an accident and so the community's focus has been to discover ideal kagome antiferromagnets where it is present and study their properties. I will argue it is not an accident and that locality and, for example, a mirror symmetry are enough to guarantee frustration. In the process, I will uncover a rich theory of distorted kagome antiferromagnets, showing their ground states map onto triangulated surfaces with (origami) or without (kirigami) holes. I will show the exchange constants J_ij behave like a background gauge field whose geometry can determine some of the zero modes. From a different perspective, I will further show there are zero modes in the spin wave spectra determined by a topological classification of Maxwell counting by extending the 10-fold way classification of Hermitian matrices that underpin topological insulators to non-Hermitian matrices. I will conclude by applying the theory to two materials and demonstrate explicitly the existence of either flat bands (Cs_2ZrCu_3F_{12}) and line-degeneracies (Cs_2CeCu_3F_{12}) in the spin wave spectra and how this relates to the curvature and folding modes in the associated triangulated surface that characterize their ground states.

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Michael Lawler, Cornell
Seminar Room 0.03, ETP
Contact: Simon Trebst