  Quantum phase transition from the N\'eel to the dimer states in an
antiferromagnetic(AF) Heisenberg model on square lattice is studied. We
introduce a control parameter $\alpha$ for the exchange coupling which connects
the N\'eel ($\alpha=0$) and the dimer ($\alpha=1$) states. We employ the $CP^1$
(the Schwinger boson) representation of the $s={1\over 2}$ spin operator and
integrate out the half of the $CP^1$ variables at odd sites and we obtain a
$CP^1$ nonlinear $\sigma$ model. The effective coupling constant is a function
of $\alpha$ and at $\alpha=0$ the $CP^1$ model is in the ordered phase which
corresponds to the N\'eel state of the AF Heisenberg model. A phase transition
to the dimer state occurs at a certain critical value of $\alpha_C$ as $\alpha$
increases. In the N\'eel state, the dynamical composite U(1) gauge field in the
$CP^1$ model is in a Higgs phase and low-energy excitations are gapless spin
wave. In the dimer phase, a confinement phase of the gauge theory is realized
and low-energy excitations are $s=1$ magnons. For the critical point, we argue
that a deconfinement phase, which is similar to the Coulomb phase in 3 spatial
dimensions, is realized and $s={1\over 2}$ spinons appear as low-energy
excitations.
