Fragmented Many-body States of Spin-2 Bose Gas

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.\ We construct the exact ground states and compare them with the angular-averaged polar and cyclic states.\ The angular-averaged polar states fail to retrieve the exact eigenstate at $N$ $\ge$ $6$ 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.