Landau-Ginzburg Theory of Tetragonal Hastatic Order: Application to URu₂Si₂

Hidden order in URu₂Si₂ remains a compelling mystery long after its discovery. We revisit the hastatic order proposal of spinorial hybridization within Landau-Ginzburg theory. Rather than a single spinorial order parameter breaking double-time-reversal symmetry, we find two vectorial orders: the expected composite order with on-site moments, and a new quantity capturing symmetries broken solely by the spinorial nature. We also address the effect of fluctuations and disorder on the tetragonal symmetry breaking, explaining the absence of in-plane moments and predicting transitions in transverse field.