Minima of multi-Higgs potentials with triplets of $\Delta(3n^2)$ and $\Delta(6n^2)$

Abstract

I present a list of minima for 3 Higgs doublet models and 6 Higgs doublet models that are invariant under the discrete symmetries $\Delta(3n^2)$ and $\Delta(6n^2)$. I use the invariant approach formalism on the scalar sector and, with relevant Spontaneous CP-odd invariants, determine if the minima lead to Spontaneous CP violation. I identify in which cases the VEVs have calculable phases, finding several new cases of Spontaneous Geometrical CP Violation, including the first cases for 6 Higgs doublet models.