Type-B Goldstone boson ($⟨[Q_1,Q_2]⟩\ne 0$)

A gapless mode associated with a canonically paired pair of broken symmetry generators. In an isotropic ferromagnet, the nonzero expectation of $[S^x,S^y]=i{S}^z$ makes two transverse coordinates one dynamical pair, giving one quadratic magnon branch. Broken-generator counting without this pairing would incorrectly predict two independent modes. This contrasts with the linear phase mode of a superfluid.