  The ground states of Bose-Einstein condensates of spin-2 bosons are
classified into three distinct (ferromagnetic, ^^ ^^ antiferromagnetic", and
cyclic) phases depending on the s-wave scattering lengths of binary collisions
for total-spin 0, 2, and 4 channels. Many-body spin correlations and magnetic
response of the condensate in each of these phases are studied in a mesoscopic
regime, while low-lying excitation spectra are investigated in the hermodynamic
regime. In the mesoscopic regime, where the system is so tightly confined that
the spatial degrees of freedom are frozen, the exact, many-body ground state
for each phase is found to be expressed in terms of the creation operators of
pair or trio bosons having spin correlations. These pairwise and trio-wise
units are shown to bring about some unique features of spin-2 BECs such as a
huge jump in magnetization from minimum to maximum possible values and the
robustness of the minimum-magnetization state against an applied agnetic field.
In the thermodynamic regime, where the system is spatially uniform, low-lying
excitation spectra in the presence of magnetic field are obtained analytically
using the Bogoliubov approximation. In the ferromagnetic phase, the excitation
spectrum consists of one Goldstone mode and four single-particle modes. In the
antiferromagnetic phase, where spin-singlet ^^ ^^ pairs" undergo Bose-Einstein
condensation, the spectrum consists of two Goldstone modes and three massive
ones, all of which become massless when magnetic field vanishes. In the cyclic
phase, where boson ^^ ^^ trios" condense into a spin-singlet state, the
spectrum is characterized by two Goldstone modes, one single-particle mode
having a magnetic-field-independent energy gap, and a gapless single-particle
mode that becomes massless in the absence of magnetic field.
