We develop Bogoliubov theory of spin-1 and spin-2 Bose-Einstein condensates
(BECs) in the presence of a quadratic Zeeman effect, and derive the
Lee-Huang-Yang (LHY) corrections to the ground-state energy, sound velocity,
and quantum depletion. We investigate all the phases of spin-1 and spin-2 BECs
that can be realized experimentally. We also examine the stability of each
phase against quantum fluctuations and the quadratic Zeeman effect.
Furthermore, we discuss a relationship between the number of symmetry
generators that are spontaneously broken and that of Nambu-Goldstone (NG)
modes. It is found that in the spin-2 nematic phase there are special
Bogoliubov modes that have gapless linear dispersion relations but do not
belong to the NG modes.Comment: v3: 62 pages, 18 figure