Classifying Novel Phases of Spinor Atoms

TL;DR

This paper introduces a classification scheme for many-body states of bosonic spinor atoms based on their spin symmetries, enabling analysis of collective modes and topological excitations, with applications to spin-2 and spin-3 atoms.

Contribution

It presents a novel symmetry-based classification method for spinor atom states, linking spin configurations to polyhedral geometries and analyzing their collective excitations.

Findings

Identified ferromagnetic and nematic phases for spin-2 atoms.

Discovered polyhedral symmetry states for spin-3 atoms.

Provided a geometric framework for classifying spinor atom states.

Abstract

We consider many-body states of bosonic spinor atoms which, at the mean-field level, can be characterized by a single-particle wave function. Such states include BEC phases and insulating Mott states with one atom per site. We describe and apply a classification scheme that makes explicit spin symmetries of such states and enables one to naturally analyze their collective modes and topological excitations. Quite generally, the method allows classification of a spin F system as a polyhedron with 2F vertices. After discussing the general formalism we apply it to the many-body states of bosons with hyperfine spins two and three. For spin-two atoms we find the ferromagnetic state, a continuum of nematic states, and a state having the symmetry of the point group of the regular tetrahedron. For spin-three atoms we obtain similar ferromagnetic and nematic phases as well as states having symmetries of various types of polyhedra with six vertices: the hexagon, the pyramid with pentagonal base, the prism, and the octahedron.