  Divergence exponents of the first-order quantum correction of a
two-dimensional hard-sphere Bose atoms are obtained by an effective field
theory method. The first-order correction to the ground-state energy density
with respect to the zeroth-order is given by
  $\cale_1/\cale_0 \sim |D-2|^{-\al}|\ln\gamma|^{-\al'}$, where $D$ is the
spatial dimension, and $\gamma$ is the gas parameter ($\gamma=n a^D$). As $D
\to 2$, $\al =\al'=1$. We show that the first-order quantum correction of the
energy density is not perturbative in low dimensions of $D < 2.2$ regardless of
any gas parameter which is much less that 1.
