Title: Spinor Bose-Einstein condensates: self-consistent symmetries and characterization

Abstract: Quantum many-body systems with spin degree of freedom may exhibit novel phases and emergent phenomena that can only described beyond mean-field theories. In this work, we present a generic and systematic method to fully determine the variational perturbations of a mean-field solution of interacting spinor systems with rotational symmetry. The method is based in a generalization of the Majorana stellar representation for quantum mixed states and group symmetry arguments. We apply the approach using the system of the spinor Bose Einstein condensates (BECs) with spin 1 and 2. To further exemplify the advantages of the method, we calculate the phase diagram of a spin-2 BEC at finite temperatures.