Title: Phase characterization of spinor Bose-Einstein condensates: a Majorana stellar representation approach

Abstract: Many-body systems with spin degree of freedom may exhibit emergent phenomena described only by beyond mean-field (MF) theories. Here we present a rigorous method to determine the variational perturbations for the MF solution of an interacting spinor system with rotational symmetries. It is based on a generalization of the Majorana stellar representation for quantum mixed states, and it is amenable to any variational method with self-consistent symmetries and for any open ensemble of spinor-like particles. As an application of the formalism, we characterize the allowed phases in spin 1 and 2 Bose-Einstein condensates and calculate the finite-temperature phase diagram of spin-2 condensates.