Fragmented many-body states of a spin-2 Bose gas

Abstract

We investigate the fragmented many-body ground states of a spin-2 Bose gas in zero magnetic field. We point out that the exact ground state is not simply an average over rotationally-invariant mean-field states, in contrast to the spin-1 case with even number of particles $N$. While for some certain parameters the exact ground state is an averaged mean-field state like in the spin-1 case, for other parameters this is not so. We construct the exact ground states and compare them with the angular-averaged polar and cyclic states. The angular-averaged polar states in general fail to retrieve the exact eigenstate at $N\ensuremath{\ge}6$ while angular-averaged cyclic states sustain only for $N$ with a multiple of 3. We calculate the density matrices and two-particle density matrices to show how deviant the angular-averaged state is from the exact one.