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Stability and Absence of a Tower of States in Ferrimagnets

Antiferromagnets and ferromagnets are archetypes of the two distinct (type-A and type-B) ways of spontaneously breaking a continuous symmetry. Although type-B Nambu--Goldstone modes arise in various systems, the ferromagnet was considered pathological due to the stability and symmetry-breaking nature of its exact ground state. However, here we show that symmetry-breaking in ferrimagnets closely resembles the ferromagnet. In particular, there is an extensive ground state degeneracy, there is no Anderson tower of states, and the maximally polarized ground state is thermodynamically stable. Our results are derived analytically for the Lieb--Mattis ferrimagnet and numerically for the Heisenberg ferrimagnet. We argue that these properties are generic for type-B symmetry-broken systems, where the order parameter operator is a symmetry generator.