Quantum Rotor Theory of Systems of Spin-2 Bosons

Abstract

We consider quantum phases of tightly-confined spin-2 bosons in an external field under the presence of rotationally-invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations about fragmented states, which cannot be accessed within standard Bogoliubov theory, can be obtained. In the spatially extended system in the thermodynamic limit there exists a mean-field ground state degeneracy between a family of nematic states for appropriate interaction parameters. It has been established that quantum fluctuations lift this degeneracy through the mechanism of order-by-disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in the full quantum treatment of the analogous single-spatial mode problem with finite particle number it is known that, due to symmetry restoring fluctuations, there is a unique ground state across the entire nematic region of the phase diagram. Within the established rotor framework we investigate the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has previously received little attention. By investigating wave function overlaps we do not find any signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated by this we consider an alternative external potential which breaks less symmetry than the quadratic Zeeman field. For this case we do find the phenomenon of order-by-disorder in the fully quantum system. This is established within the rotor framework and with exact diagonalization.