Spin nematics revisited

Abstract
Biquadratic spin 1 Heisenberg spin systems can be constructed exhibiting spin nematic order in higher dimensions. In terms of the original spin degrees of freedom, the spontaneous nematic symmetry breaking generates a Z ₂ gauge invariance. Using a generalized Holstein-Primakoff transformation for the underlying U(3) dynamical algebra, we calculate the spin dynamical form factor. Although spin is not a gauge singlet, we find form factor to be finite at finite q and $ omega $, contrary to our expectations regarding the presence of a energy scale protecting the gauge invariance. This result appears to be perturbatively stable.