  We present a theory of the anisotropy tuned quantum phase transition between
spin nematic and spin-Peierls phases in S=1 systems with significant
bi-quadratic exchange interactions. Based on quantum Monte Carlo studies on
finite size systems, [K. Harada et al., J. Phys. Soc. Jpn. 76, 013703 (2007)]
it has been proposed that this phase transition is second order with new
deconfined fractional excitations that are absent in either of the two phases
[T. Grover and T. Senthil, Phys. Rev. Lett. 98, 247202 (2007)]. The possibility
of a weak first order transition, however, cannot be ruled out. To elucidate
the nature of the transition, we construct a large-N SO(3N) model for this
phase transition and find in the $N\to\infty$ limit that the transition is
generically of first order. Furthermore, we find a critical point in the 1D
limit, where two transition lines, separating spin nematic, ferromagnetic, and
spin-Peierls phases, meet. Our study indicates that the spin nematic phase is
absent in 1D, while its correlation length diverges at the critical point.
Predictions for $^{23}$Na atoms trapped in an optical lattice, where this
quantum phase transition naturally arises, are discussed.
